Komplex Rendszerek Kutatócsoport
https://wigner.hu/hu/elmeleti-szilardtest-fizikai-osztaly/komplex-rendszerek-kutatocsoport
hu2019_Complex Systems Research Group
https://wigner.hu/hu/node/1457
<span class="field field--name-title field--type-string field--label-hidden">2019_Complex Systems Research Group</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2019</strong></h4>
<p>The research activity of Complex Systems research group in 2019 covered various topics in the field of cooperative behavior, phase transitions and nonequilibrium dynamics of systems with many degrees of freedom.</p>
<p><b>Entanglement entropy of random partitioning.</b> — We studied the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system, we considered a finite, connected, hypercubic domain of linear extent L, the points of which belong to the subsystem with probability p. The leading contribution to the average entanglement entropy is found to scale proportionally to the volume, with an additive logarithmic correction term. In one dimension, the prefactor of the correction is determined by the central charge of the model and a universal function of p. In two dimensions, the prefactor was found to have a different functional form of p below and above the percolation threshold.</p>
<p><b>Reentrant random quantum Ising antiferromagnet. </b>— We considered the quantum Ising chain with uniformly distributed random antiferromagnetic couplings and transverse fields, in the presence of a homogeneous longitudinal field. Using different numerical techniques (DMRG, combinatorial optimization and strong-disorder RG methods) we explored the phase diagram, which consists of an ordered and a disordered phase, see Fig. 1. At one end of the transition line, an infinite-disorder quantum fixed point can be found, while at the other end, a classical, random first-order transition point is located. Close to this fixed point, there is a reentrant ordered phase, which is the result of quantum fluctuations by means of an order through disorder phenomenon.</p>
<img alt="Complex_1" data-entity-type="file" data-entity-uuid="5e06882f-310a-49ad-96ec-0c89112c7a7a" src="https://wigner.hu/sites/default/files/inline-images/complex1.jpg" width="500" class="align-center" />
<p><i><b>Figure 1. </b>Phase diagram of the random quantum Ising antiferromagnet with random transverse fields distributed uniformly in the range [Γ<sub>0</sub>,2Γ<sub>0</sub>] and a homogeneous longitudinal field of strength h. Finite-size transition points were calculated by the DMRG method. The dashed line shows the expected phase boundary in the thermodynamic limit.</i></p>
<p><b>Population boundary across an environmental gradient: effects of quenched disorder.</b> —Population boundary is a classic indicator of climatic response in ecology. We captured the effects of quenched heterogeneities on the ecological boundary with the disordered contact process in one- and two dimensions with a linear spatial trend in the local control parameter. We applied the strong-disorder renormalization group method to determine the sites occupied with an O(1) probability in the stationary state, readily yielding the population front's position as the outermost site locally as well as globally for the entire boundary. We showed that under a quasistatic change of the global environment, mimicking climate change, the front advances intermittently: long quiescent periods are interrupted by rare but long jumps. The characteristics of this intermittent dynamics are found to obey universal scaling laws in terms of the gradient, conjectured to be related to the correlation-length exponent of the model. Our results suggest that current observations might misleadingly show little to no climate response for an extended period of time, concealing the long-term effects of climate change. In the same model, we have found by numerical simulations that the hull of the connected region, illustrated in Fig. 2, is a fractal with a dimension 7/4. Its width and length changes with the gradient according to universal scaling laws, that are characteristic for the percolation transition. The results suggest that percolation theory is a powerful tool for understanding the structure of range margins in a broad variety of real-life scenarios, including those in which the environmental gradient is combined with fine-scale heterogeneity.</p>
<img alt="Complex2" data-entity-type="file" data-entity-uuid="27628e68-da56-4f64-aebf-3fd85689848e" src="https://wigner.hu/sites/default/files/inline-images/complex2.jpg" width="500" class="align-center" />
<p><i><b>Figure 2. </b>Snapshot of the contact process with a gradient in the vertical direction. The largest percolation cluster and its hull are marked in green and red, respectively.</i></p>
<p><b>Critical dynamics of the Kuramoto model on sparse random networks.</b> — We considered the Kuramoto model on sparse random networks such as the Erdős-Rényi graph or its combination with a regular two-dimensional lattice, and studied the dynamical scaling behavior of the model at the synchronization transition by large-scale, massively parallel numerical integration. By this method, we obtained an estimate of the critical coupling strength more accurate than obtained earlier by finite-size scaling of the stationary order parameter. Our results confirm the compatibility of the correlation-size and the temporal correlation-length exponent with the mean-field universality class. However, the scaling of the order parameter exhibits corrections much stronger than those of the Kuramoto model with all-to-all coupling, making thereby an accurate estimation of the order-parameter exponent hard. We find furthermore that, as a qualitative difference to the model with all-to-all coupling, the effective critical exponents involving the order-parameter exponent show a non-monotonic approach toward the asymptotic value.</p>
<p><b>Laser-induced distortion of band structure in solids.</b> — We have considered a spatially periodic (cosine) potential as a model for a crystalline solid that interacts with a harmonically oscillating external electric field (which represents a strong laser field). The Hamiltonian of this system is periodic both in space and time, and the associated single-particle Schrödinger equation has been described non-perturbatively, with respect to both of the interactions. The unperturbed (laser-free) problem is related to a Mathieu-type differential equation, whose Floquet-Bloch solutions, with the well-known stability chart, deliver the electronic band structure. By developing a non-perturbative analytic method, based on the cycle-averaged laser-dressed lattice potential, we can incorporate the effect of a high-intensity laser field up to infinite order. We have demonstrated that by changing the (moderately large) laser intensity, the width of the original zero-field band gaps can be drastically modified. Our formulae also include the special cases when the external field causes the band gaps to disappear, as is illustrated in Fig. 3, thus, at certain external field intensities, the system may become completely conductive. Such a phenomenon may perhaps be a physical basis for constructing laser intensity meters and switches.</p>
<img alt="Complex_3" data-entity-type="file" data-entity-uuid="caf9c782-d160-4b15-9153-a37d45d35039" src="https://wigner.hu/sites/default/files/inline-images/complex3.jpg" width="500" class="align-center" />
<p><em>Figure 3. Laser intensity-dependence of the border lines of the second gap in the energy spectrum of the electrons, interacting jointly with the static cosine potential and with a laser field. The upper (lower) curve shows the change of the upper (lower) border of the second gap. We assumed that the wavelength of the laser is 2000 times larger than the lattice constant, and chosen a Ti:Sa laser field, up to intensities 2.5x10<sup>13 </sup>W/cm<sup>2</sup>. The width of the gap is determined by the difference of the ordinates on the two curves, and, as clearly seen, it may disappear at certain intensities.</em></p>
<p> </p>
</div>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/124" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Pentek Csilla</span></span>
<span class="field field--name-created field--type-created field--label-hidden">h, 05/25/2020 - 14:19</span>
Mon, 25 May 2020 12:19:19 +0000Pentek Csilla1457 at https://wigner.hu2018_Complex Systems Research Group
https://wigner.hu/hu/node/955
<span class="field field--name-title field--type-string field--label-hidden">2018_Complex Systems Research Group</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2018</strong></h4>
<p>The research activity of Complex Systems research group in 2018 covered various topics in the field of cooperative behavior, phase transitions and nonequilibrium dynamics of systems with many degrees of freedom. </p>
<p><strong>Strong-disorder RG approach — short review of recent developments.</strong> — The strong-disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [F. Iglói, C. Monthus, Phys. Rep. 412, 277 (2005)]. This year we have written a colloquium paper to give an overview of these various recent developments. In the field of quantum disordered models, recent progress concerning finite-disorder fixed points for short-ranged models in higher dimensions d > 1, strong-disorder fixed points for long-ranged models, scaling of the entanglement entropy in critical ground states and after quantum quenches, the RSRG-X procedure to construct the whole set of excited states and the RSRG-t procedure for the unitary dynamics in many-body-localized phases, the Floquet dynamics of periodically driven chains, the dissipative effects induced by the coupling to external baths, and Anderson localization models. In the field of classical disordered models, new applications include the contact process for epidemic spreading, the strong-disorder renormalization procedure for general master equations, the localization properties of random, elastic networks, and the synchronization of interacting non-linear dissipative oscillators. Application of the method for aperiodic (or deterministic)<br />
disorder is also reviewed.</p>
<p><br />
<strong>Transverse-spin correlations of the random transverse-field Ising model.</strong> — The random transverse-field Ising model is the prototype of random quantum magnets, which is defined by the Hamiltonian:<br />
<img alt="rj1" data-entity-type="file" data-entity-uuid="e6d53a44-2aad-43a3-9741-82302aa401f9" height="77" src="https://wigner.hu/sites/default/files/inline-images/rj1%20.jpg" width="343" /><br />
where <span style="font-size:11.0pt"><span style="font-family:"Times New Roman","serif"">σ</span></span><sub><span style="font-size:11.0pt"><span style="font-family:CMR10">i</span></span></sub><sup><span style="font-size:11.0pt"><span style="font-family:CMR10">x,z</span></span></sup> are Pauli-matrices, i, j denote sites of the lattice and ⟨ij⟩ refers to nearest neighbors. The couplings Jij and transverse fields hi are independent random numbers. The critical behavior of the model in finite dimensional lattices is governed by infinite-disorder fixed points, several properties of which have already been calculated by the use of the strong-disorder renormalization group (SDRG) method. Here, we have extended these studies and calculated the connected transverse-spin correlation function:<br />
<img alt="rj2" data-entity-type="file" data-entity-uuid="3334010a-be53-47e8-85ce-1cc8875a0259" height="34" src="https://wigner.hu/sites/default/files/inline-images/rj2.jpg" width="337" /><br />
where the overbar denotes an average over quenched disorder. We have used free-fermionic techniques in d = 1 and a numerical implementation of the SDRG method in d = 1, 2, and 3 dimensions. At the critical point, an algebraic decay of the form ~ <span style="font-size:11.0pt"><span style="font-family:CMR10">1/r</span></span><sup><span style="font-size:11.0pt"><span style="font-family:"Cambria Math","serif"">η</span></span></sup> is found, with a decay exponent being approximately η ≈ 2+2d.<br />
<br />
<strong>Quantum XX model with competing short and long-range interactions. </strong>— We considered the quantum XX model with competing short and global-range interactions in a one-dimensional lattice, defined by the Hamiltonian:<br />
<img alt="rj3" data-entity-type="file" data-entity-uuid="03717403-0644-4d61-acff-f578598399f7" height="78" src="https://wigner.hu/sites/default/files/inline-images/rj3.jpg" width="608" /><br />
The nearest-neighbor coupling constant and the strength of the transverse field are denoted by J and h, respectively, and the last term of the r.h.s. represents a global-range antiferromagnetic interaction of strength ε. It is expressed as the square of the staggered magnetization operator:<br />
<img alt="rj4" data-entity-type="file" data-entity-uuid="0ab3123a-5234-4e8e-8a45-f0e5d03b9bcc" height="66" src="https://wigner.hu/sites/default/files/inline-images/rj4.jpg" width="528" /><br />
This model is equivalent to a Bose-Hubbard model with cavity-mediated global-range interactions in the hard-core-boson limit, which has experimental relevance in terms of cold atoms in an optical lattice in the presence of a high-finesse optical resonator, an optical cavity. Using fermionic techniques, the problem was solved exactly in one dimension in the thermodynamic limit. The ground-state phase diagram consists of two ordered phases: ferromagnetic (F) and antiferromagnetic (AF), as well as an XY phase having quasi-long-range order, see Fig. 1. We have also studied quantum relaxation after sudden quenches. Quenching from the AF phase to the XY region, remanent AF order is observed below a dynamical transition line. In the opposite quench, from the XY region to the AF phase beyond a static metastability line, AF order arises on top of remanent XY quasi-long-range order, which corresponds to a dynamically generated supersolid state in the equivalent Bose-Hubbard model with hard-core bosons.<br />
<br />
<strong>Entanglement entropy of disordered quantum wire junctions. </strong>— The entanglement properties of extended quantum systems have attracted much interest in the recent decade. One reason for this is that various entanglement measures turned out be sensitive to whether the underlying model is critical or not, moreover, some of these showed universal scaling in critical points. For a subsystem A of a closed system in a pure state, the natural entanglement measure is the entanglement entropy, which is the von Neumann entropy of the reduced density matrix corresponding to the subsystem. An important question is how the inhomogeneities, which break translational invariance, and which are present almost inevitably in real systems, affect the entanglement properties. As a contribution to this field, we considered different disordered lattice models composed of M linear chains glued together in a star-like manner, and studied the scaling of the entanglement between one arm and the rest of the system using a numerical strong-disorder renormalization group (SDRG) method. We pointed out that the random XX model and the free-fermion (FF) model with random nearest-neighbor hopping obey different SDRG rules at a junction as opposed to a linear geometry, which is illustrated in Fig. 2. For all studied models, the random transverse-field Ising model (RTIM), the XX spin model, and the FF model, the average entanglement entropy is found to increase with the length L of the arms according to the form <span lang="EN-US" style="font-size:11.0pt" xml:lang="EN-US" xml:lang="EN-US"><span style="font-family:"Times New Roman","serif"">S(L)=c<sub>eff</sub>/6lnL </span></span> + const. For the RTIM and the XX model, the effective central charge ceff is universal with respect to the details of junction, and only depends on the number M of arms. Interestingly, for the RTIM, ceff decreases with M, whereas for the XX model it increases. For the latter model, the numerical estimates fit accurately to a form linear in 1/M: <span lang="EN-US" style="font-size:11.0pt" xml:lang="EN-US" xml:lang="EN-US"><span style="font-family:"Times New Roman","serif"">c<sub>eff</sub>(M)</span></span>=2ln2(1-1/M). For the free-fermion model, ceff depends also on the details of the junction, which is related to the sublattice symmetry of the model. In this case, both increasing and decreasing tendency with M can be realized with appropriate junction geometries. We also established upper bounds on the average entanglement entropy of a chain of length L for all the three models under study, which hold universally, irrespective of the other subsystem to which the chain is coupled.<br />
<br />
<strong>Network-based prediction of protein interactions. </strong>— As biological function emerges through interactions between a cell's molecular constituents, understanding cellular mechanisms requires us to catalogue all physical interactions between proteins. Despite spectacular advances in high-throughput mapping, the number of missing human protein-protein interactions (PPIs) continues to exceed the experimentally documented interactions. Computational tools that exploit structural, sequence or network topology information are increasingly used to fill in the gap, using the patterns of the already known interactome to predict undetected, yet biologically relevant interactions. Such network-based link prediction tools rely on the Triadic Closure Principle (TCP), stating that two proteins likely interact if they share multiple interaction partners. TCP is rooted in social network analysis, namely the observation that the more common friends two individuals have, the more likely that they know each other. We offered direct empirical evidence across multiple datasets and organisms that, despite its dominant use in biological link prediction, TCP is not valid for most protein pairs. We showed that this failure is fundamental - TCP violates both structural constraints and evolutionary processes. This understanding allowed us to propose a link-prediction principle, consistent with both structural and evolutionary arguments, that predicts yet uncovered protein interactions based on paths of length three (L3). A systematic computational cross-validation showed that the L3 principle significantly outperformed existing link-prediction methods. To experimentally test the L3 predictions, we performed both large-scale high-throughput and pairwise tests, finding that the predicted links test positively at the same rate as previously known interactions, suggesting that most (if not all) predicted interactions are real. Combining L3 predictions with experimental tests provided new interaction partners of FAM161A, a protein linked to retinitis pigmentosa, offering novel insights into the molecular mechanisms that lead to the disease. Because L3 is rooted in a fundamental biological principle, we expect it to have a broad applicability, enabling us to better understand the emergence of biological function under both healthy and pathological conditions.</p>
<p><strong>Collective nonlinear Thomson back-scattering for generating phase-controlled isolated attosecond pulses in the nm wavelength range. </strong>— We have studied the collectively emitted radiation of a relativistic electron bunch of 10<sup>6</sup> – 10<sup>8 </sup>electrons colliding with an intense femtosecond (few-cycle) near-infrared laser pulse. By analytically solving the equation of motion of the electrons interacting with the incoming laser field of arbitrarily high intensity, the exact radiation field stemming from Thomson back-scattering has been calculated in the head-on collision geometry. On the basis of our results, the collective spectrum (containing very high-order harmonics) and the corresponding temporal shape of the radiation emitted by a mono-energetic electron bunch has been determined. It has turned out that for certain, realistic input parameters, single-cycle isolated pulses of ca. 20 attosecond (as) duration can be generated in the XUV – soft x-ray spectral range, including the 2.33–4.37 nm water window. We have also shown that the generated collective radiation is almost linearly polarized, and it is extremely well collimated around the initial velocity of the electron bunch. Moreover, this radiation has a considerable intensity and its carrier envelope phase difference (CEP) is locked to that of the incoming femtosecond laser pulse. The results of the present study allow us to propose a novel source of isolated attosecond XUV – soft x-ray pulses with a well-controlled CEP. Such sources of radiation may be of importance because isolated attosecond XUV pulses make possible to investigate the real-time electron dynamics in atoms, molecules and solids experimentally. Besides, the CEP of the incoming femtosecond laser pulse affects various processes in atomic or molecular systems on this time scale, as has been observed in most of the pioneering experiments. The proposed novel source of isolated attosecond pulses may have several scientific applications, e.g. in performing pump–probe experiments on the attosecond time scale. Figure 3 illustrates the CEP phase locking which manifests itself in the temporal evolution of the isolated attosecond pulses generated by the Thomson back-scattering of the incoming single-cycle laser pulses with different CEP values.<br />
<br />
<img alt="rj5" data-entity-type="file" data-entity-uuid="997d86d6-5ac9-4ef7-b42c-d2088f5f277e" src="https://wigner.hu/sites/default/files/inline-images/rj5.jpg" /><br />
<br />
<em><strong>Figure 1.</strong> Phase diagram of the quantum XX model with cavity-induced global-range interactions of strength ε = 1. The color codes indicate the value of the staggered magnetization, x, and that of the longitudinal magnetization, mz. <br />
<br />
<img alt="rj6" data-entity-type="file" data-entity-uuid="db5a91b8-f906-472c-9e75-284271e4c8e1" height="222" src="https://wigner.hu/sites/default/files/inline-images/rj6.jpg" width="668" /></em><br />
<br />
<em><strong>Figure 2.</strong> SDRG steps for the XX model (XX) and free fermions (FF) in the case of two elementary geometries. The sites coupled by the strongest bond (shown in red) are eliminated, while the remaining sites are connected by a weak, effective coupling obtained perturbatively. For the linear configuration the steps for the XX and FF models essentially agree with each other, while for the T shaped geometry they differ.</em><br />
<br />
<img alt="rj7" data-entity-type="file" data-entity-uuid="75bd6ff8-40d8-423b-b887-48497f2da26c" height="435" src="https://wigner.hu/sites/default/files/inline-images/rj7.jpg" width="680" /><br />
<br />
<em><strong>Figure 3. </strong>Temporal pulse shapes of the isolated attosecond pulses (at distance R<sub>0</sub>=2 m from the interaction region), stemming from nonlinear Thomson back-scattering along the polar angle of 180°, for different values of the carrier-envelope phase difference (CEP) of the near-infrared (NIR) laser pulse given in the legend. The inset shows the incoming NIR pulse shapes of different CEP with the corresponding colors. We have considered an 8nm electron bunch of 108 electrons, whose initial relativistic factor has been assumed to be </em><i><span lang="EN-US" style="font-size:12.0pt" xml:lang="EN-US" xml:lang="EN-US"><span style="font-family:"Times New Roman","serif""><span style="color:black">γ<sub>0</sub></span></span></span></i><em>=10. The assumed parameters of the counter-propagating, almost single-cycle laser pulse are </em><i><span lang="EN-US" style="font-size:12.0pt" xml:lang="EN-US" xml:lang="EN-US"><span style="font-family:"Times New Roman","serif""><span style="color:black">λ<sub>L</sub>=800 nm, E<sub>0</sub>=4×10<sup>12</sup> </span></span></span></i><em> V/m.This figure shows that the CEP of the attosecond pulse perfectly follows the CEP of the NIR laser pulse with a phase difference of π. This very simple relationship makes the CEP of these attosecond pulses easily controllable through the CEP of the NIR laser pulse, which is expected to have an importance in attosecond pump-probe experiments. </em></p>
</div>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/171" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Werovszky Veronika</span></span>
<span class="field field--name-created field--type-created field--label-hidden">cs, 08/08/2019 - 13:33</span>
Thu, 08 Aug 2019 11:33:27 +0000Werovszky Veronika955 at https://wigner.hu2017_Complex Systems Research Group
https://wigner.hu/hu/node/1456
<span class="field field--name-title field--type-string field--label-hidden">2017_Complex Systems Research Group</span>
<div class="clearfix text-formatted field field--name-body field--type-text-with-summary field--label-hidden field__item"><h4><strong>2017</strong></h4>
<p>The research activity of Complex Systems research group in 2017 covered various topics in the field of cooperative behavior, phase transitions and nonequilibrium dynamics of systems with many degrees of freedom. </p>
<p><strong>Entanglement entropy of composite quantum spin chains.</strong> — The entanglement entropy in clean, as well as in random critical quantum spin chains is well known to have a logarithmic scaling with the size of the subsystem. We considered a composite, antiferromagnetic XX chain that consists of a clean and a random part, and found a double-logarithmic scaling of the half-chain entanglement entropy: S∼lnln(<em>L</em>). We also considered the case, when the disorder penetrates into the homogeneous part in such a way that its strength decays with the distance <em>l</em> as ∼<em>l</em>−<em>κ</em>. For <em>κ</em><1/2, the entropy scales logarithmically with a modified prefactor as S(<em>κ</em>)≃(1−2<em>κ</em>)S(<em>κ</em>=0), while for <em>κ</em>≥1/2, we recover the double-logarithmic scaling. These results were explained by strong-disorder RG arguments. We also studied the half-chain entanglement entropy across a symmetric, extended random defect, where the strength of disorder decays algebraically on both sides of the interface. In the whole regime <em>κ</em>≥0, we found a logarithmic scaling of the entropy, but the variation of the prefactor with <em>κ </em>is non-monotonic and discontinuous at <em>κ</em>=1/2. </p>
<p><strong>Quantum relaxation of lattice bosons with cavity-induced interactions.</strong> —The coupling of cold atoms to the radiation field within a high-finesse optical resonator induces long-range interactions which can compete with an underlying optical lattice. The interplay between short- and long-range interactions gives rise to new phases of matter including supersolidity (SS) and density waves (DW). We have shown that for hard-core bosons in one dimension, the ground-state phase diagram (see Fig. 1) and the quantum relaxation after sudden quenches can be calculated exactly in the thermodynamic limit. Remanent DW order is observed for quenches from a DW ground state into the superfluid (SF) phase below a dynamical transition line. After sufficiently strong SF to DW quenches beyond a static metastability line, DW order emerges on top of remanent SF order, giving rise to a dynamically generated supersolid state. </p>
<p><strong>Proof of phase transition in homogeneous systems of interacting bosons.</strong> — Using the rigorous path integral formalism of Feynman and Kac, we proved London's eighty-year-old conjecture that during the superfluid transition in liquid helium, Bose-Einstein condensation (BEC) takes place. The result is obtained by proving first that, at low enough temperatures, macroscopic permutation cycles appear in the system, and then showing that this implies BEC. We found also that, in the limit of zero temperature, the infinite cycles cover the whole system, while BEC remains partial. Via the equivalence of 1/2 spins and hard-core bosons the method extends to lattice models. We showed that, at low enough temperatures, the spin-1/2 axially anisotropic Heisenberg models, including the isotropic ferro- and antiferromagnet and the XY model, undergo magnetic ordering. </p>
<p><img alt="f1" data-entity-type="file" data-entity-uuid="3758d803-3c8d-4ae7-bb70-1161b76f38ad" height="328" src="https://wigner.hu/sites/default/files/inline-images/K%C3%A9perny%C5%91fot%C3%B3%202018-11-24%20-%2020.49.35.png" width="654" /></p>
<p><strong><em>Figure 1.</em></strong><em> Phase diagram of the Bose-Hubbard model with cavity-induced infinite-range interactions. </em><em>T, </em><em>μ, ε, and x denote the tunneling constant, the chemical potential, the strength of cavity-induced interactions, and the density-wave order parameter (imbalance), respectively. MI, SF, and DW stand for Mott insulator, superfluid, and density wave, respectively. </em></p>
<p><strong>Critical behavior of the contact process near an extended defect.</strong> — The contact process is a simple stochastic lattice model of epidemic spreading. We considered its inhomogeneous variant, where the deviation of the local control parameter from the bulk value tends to zero with the distance from the surface as <em>λ</em>(<em>l</em>)−<em>λ</em>(∞)=<em>Al</em>−<em>s</em>. In the marginal case, <em>s</em>=1/<em>ν</em>⊥, where <em>ν</em>⊥ is the correlation-length critical exponent, Monte Carlo simulations show a rich surface critical behavior. For weaker perturbations, <em>A</em><<em>A</em><em>c</em>, the transition is continuous and the order-parameter critical exponent varies continuously with <em>A</em>. For <em>A</em>><em>A</em><em>c</em>, the phase transition is of mixed order: the order parameter is discontinuous but, at the same time, the temporal correlation length diverges, with different exponents on the two sides of the transition. This behavior in the mixed-order regime was explained in the frame of a scaling theory.</p></div>
<span class="field field--name-uid field--type-entity-reference field--label-hidden"><span lang="" about="https://wigner.hu/hu/user/124" typeof="schema:Person" property="schema:name" datatype="" xml:lang="">Pentek Csilla</span></span>
<span class="field field--name-created field--type-created field--label-hidden">p, 05/25/2018 - 14:16</span>
Fri, 25 May 2018 12:16:59 +0000Pentek Csilla1456 at https://wigner.hu