Random fields at a nonequilibrium phase transition

Critical behavior of density-driven and shear-driven reversible-irreversible transitions in cyclically sheared vortices

Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{\mathrm {c}}$$\end{document}Bc and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc, the relaxation time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) exhibits a power-law divergence at the same \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc with nearly the same exponent.

Influence of distinct kinds of temporal disorder in discontinuous phase transitions

Based on mean-field theory (MFT) arguments, a general description for discontinuous phase transitions in the presence of temporal disorder is considered. Our analysis extends the recent findings [C. E. Fiore et al., Phys. Rev. E 98, 032129 (2018)2470-004510.1103/PhysRevE.98.032129] by considering discontinuous phase transitions beyond those with a single absorbing state. The theory is exemplified in one of the simplest (nonequilibrium) order-disorder (discontinuous) phase transitions with "up-down" Z_{2} symmetry: the inertial majority vote model for two kinds of temporal disorder. As for absorbing phase transitions, the temporal disorder does not suppress the occurrence of discontinuous phase transitions, but remarkable differences emerge when compared with the pure (disorderless) case. A comparison between the distinct kinds of temporal disorder is also performed beyond the MFT for random-regular complex topologies. Our work paves the way for the study of a generic discontinuous phase transition under the influence of an arbitrary kind of temporal disorder.

Ising universality in the two-dimensional Blume-Capel model with quenched random crystal field

Using high-precision Monte Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques, we study the effect of quenched disorder in the crystal-field coupling of the Blume-Capel model on a square lattice. We mainly focus on the part of the phase diagram where the pure model undergoes a continuous transition, known to fall into the universality class of a pure Ising ferromagnet. A dedicated scaling analysis reveals concrete evidence in favor of the strong universality hypothesis with the presence of additional logarithmic corrections in the scaling of the specific heat. Our results are in agreement with an early real-space renormalization-group study of the model as well as a very recent numerical work where quenched randomness was introduced in the energy exchange coupling. Finally, by properly fine tuning the control parameters of the randomness distribution we also qualitatively investigate the part of the phase diagram where the pure model undergoes a first-order phase transition. For this region, preliminary evidence indicate a smoothing of the transition to second-order with the presence of strong scaling corrections.

Discontinuous transitions can survive to quenched disorder in a two-dimensional nonequilibrium system

We explore the effects that quenched disorder has on discontinuous nonequilibrium phase transitions into absorbing states. We focus our analysis on the naming game model, a nonequilibrium low-dimensional system with different absorbing states. The results obtained by means of the finite-size scaling analysis and from the study of the temporal dynamics of the density of active sites near the transition point evidence that the spatial quenched disorder does not destroy the discontinuous transition.

Quenched disorder in the contact process on bipartite sublattices

We study the effects of distinct types of quenched disorder in the contact process with a competitive dynamics on bipartite sublattices. In the model, the particle creation depends on its first and second neighbors and the extinction increases according to the local density. The clean (without disorder) model exhibits three phases: inactive (absorbing), active symmetric, and active asymmetric, where the latter exhibits distinct sublattice densities. These phases are separated by continuous transitions; the phase diagram is reentrant. By performing mean-field analysis and Monte Carlo simulations we show that symmetric disorder destroys the sublattice ordering and therefore the active asymmetric phase is not present. On the other hand, for asymmetric disorder (each sublattice presenting a distinct dilution rate) the phase transition occurs between the absorbing and the active asymmetric phases. The universality class of this transition is governed by the less-disordered sublattice. Finally, our results suggest that random-field disorder destroys the phase transition if it breaks the symmetry between two active states.

Universality from disorder in the random-bond Blume-Capel model

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections which is also observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior of the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale L^{*}≈32 for the chosen parameters.

Comparing the influence of distinct kinds of temporal disorder in a low-dimensional absorbing transition model

Recently it was stated that temporal disorder constitutes a relevant perturbation in absorbing phase transitions for all dimensions. However, its effect on systems other than the standard contact process (CP), its competition with other ingredients (e.g., particle diffusion), and other kinds of disorder (besides the standard types) are unknown. In order to shed some light on the above-mentioned points, we investigate a variant of the usual CP, namely, the triplet annihilation model, in which the competition between triplet annihilation and single particle diffusion leads to an unusual phase diagram behavior, with reentrant shape and endless activity for sufficiently large diffusion rates. Two kinds of time-dependent disorder have been considered. In the former, it is introduced in the creation-annihilation parameters (as commonly considered in recent studies), whereas in the latter, the diffusion rate D is allowed to be time dependent. In all cases, the disorder follows a uniform distribution with fixed mean and width σ. Two values of σ have been considered in order to exemplify the regime of "weaker" and "stronger" temporal disorder strengths. Our results show that in the former approach, the disorder suppresses the reentrant phase diagram with a critical behavior deviating from the directed percolation (DP) universality class in the regime of low diffusion rates, while they strongly suggest that the DP class is recovered for larger hopping rates. An opposite scenario is found in the latter disorder approach, with a substantial increase of reentrant shape and the maximum diffusion, in which the reentrant shape also displays a critical behavior consistent with the DP universality class (in similarity with the pure model). In order to compare with very recent claims, the results from taking a bimodal distribution and critical behavior in the limit of strong disorder are presented. Also, the results derived from the mean-field theory are performed, presenting partial agreement with numerical results. Lastly, a comparison with the diffusive disordered CP is undertaken.

Temporal disorder does not forbid discontinuous absorbing phase transitions in low-dimensional systems

Recent papers have shown that spatial (quenched) disorder can suppress discontinuous absorbing phase transitions. Conversely, the scenario for temporal disorder is still unknown. To shed some light in this direction, we investigate its effect in three different two-dimensional models which are known to exhibit discontinuous absorbing phase transitions. The temporal disorder is introduced by allowing the control parameter to be time dependent p→p(t), either varying as a uniform distribution with mean p[over ¯] and variance σ or as a bimodal distribution, fluctuating between a value p and a value p_{l}≪p. In contrast to spatial disorder, our numerical results strongly suggest that such uncorrelated temporal disorder does not forbid the existence of a discontinuous absorbing phase transition. We find that all cases are characterized by behaviors similar to their pure (without disorder) counterparts, including bistability around the coexistence point and common finite-size scaling behavior with the inverse of the system volume, as recently proposed [M. M. de Oliveira et al., Phys. Rev. E 92, 062126 (2015)PLEEE81539-375510.1103/PhysRevE.92.062126]. We also observe that temporal disorder does not induce temporal Griffiths phases around discontinuous phase transitions, at least not for d=2.

Random field disorder at an absorbing state transition in one and two dimensions

We investigate the behavior of nonequilibrium phase transitions under the influence of disorder that locally breaks the symmetry between two symmetrical macroscopic absorbing states. In equilibrium systems such "random-field" disorder destroys the phase transition in low dimensions by preventing spontaneous symmetry breaking. In contrast, we show here that random-field disorder fails to destroy the nonequilibrium phase transition of the one- and two-dimensional generalized contact process. Instead, it modifies the dynamics in the symmetry-broken phase. Specifically, the dynamics in the one-dimensional case is described by a Sinai walk of the domain walls between two different absorbing states. In the two-dimensional case, we map the dynamics onto that of the well studied low-temperature random-field Ising model. We also study the critical behavior of the nonequilibrium phase transition and characterize its universality class in one dimension. We support our results by large-scale Monte Carlo simulations, and we discuss the applicability of our theory to other systems.

Effect of diffusion in one-dimensional discontinuous absorbing phase transitions

It is known that diffusion provokes substantial changes in continuous absorbing phase transitions. Conversely, its effect on discontinuous transitions is much less understood. In order to shed light in this direction, we study the inclusion of diffusion in the simplest one-dimensional model with a discontinuous absorbing phase transition, namely, the long-range contact process (σ-CP). Particles interact as in the usual CP, but the transition rate depends on the length ℓ of inactive sites according to 1+aℓ(-σ), where a and σ are control parameters. The inclusion of diffusion in this model has been investigated by numerical simulations and mean-field calculations. Results show that there exists three distinct regimes. For sufficiently low and large σ's the transition is, respectively, always discontinuous or continuous, independently of the strength of the diffusion. On the other hand, in an intermediate range of σ's, the diffusion causes a suppression of the phase coexistence leading to a continuous transition belonging to the directed percolation universality class.

Quenched disorder forbids discontinuous transitions in nonequilibrium low-dimensional systems

Quenched disorder affects significantly the behavior of phase transitions. The Imry-Ma-Aizenman-Wehr-Berker argument prohibits first-order or discontinuous transitions and their concomitant phase coexistence in low-dimensional equilibrium systems in the presence of random fields. Instead, discontinuous transitions become rounded or even continuous once disorder is introduced. Here we show that phase coexistence and first-order phase transitions are also precluded in nonequilibrium low-dimensional systems with quenched disorder: discontinuous transitions in two-dimensional systems with absorbing states become continuous in the presence of quenched disorder. We also study the universal features of this disorder-induced criticality and find them to be compatible with the universality class of the directed percolation with quenched disorder. Thus, we conclude that first-order transitions do not exist in low-dimensional disordered systems, not even in genuinely nonequilibrium systems with absorbing states.