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Register a new userNon-equilibrium relaxation and critical aging for driven Ising lattice gases
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We employ Monte Carlo simulations to study the non-equilibrium relaxation of driven Ising lattice gases in two dimensions. Whereas the temporal scaling of the density auto-correlation function in the non-equilibrium steady state does not allow a precise measurement of the critical exponents, these can be accurately determined from the aging scaling of the two-time auto-correlations and the order parameter evolution following a quench to the critical point. We obtain excellent agreement with renormalization group predictions based on the standard Langevin representation of driven Ising lattice gases.
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We numerically investigate the long-time behavior of the density-density auto-correlation function in driven lattice gases with particle exclusion and periodic boundary conditions in one, two, and three dimensions using precise Monte Carlo simulations. In the one-dimensional asymmetric exclusion process on a ring with half the lattice sites occupied, we find that correlations induce extremely slow relaxation to the asymptotic power law decay. We compare the crossover functions obtained from our simulations with various analytic results in the literature, and analyze the characteristic oscillations that occur in finite systems away from half-filling. As expected, in three dimensions correlations are weak and consequently the mean-field description is adequate. We also investigate the relaxation towards the nonequilibrium steady state in the two-time density-density auto-correlations, starting from strongly correlated initial conditions. We obtain simple aging scaling behavior in one, two, and three dimensions, with the expected power laws.
Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang (KPZ) equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents $alpha=0.500(5)$, $z=1.52(3)$, $beta=0.33(1)$. With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz results; (ii) in the low-density phase, curve collapse can be found to a rather good extent, with $alpha=0.497(3)$, $z=1.20(5)$, $beta=0.41(2)$, which is apparently at variance with the Bethe ansatz prediction $z=0$; (iii) on the coexistence line between low- and high- density phases, $alpha=0.99(1)$, $z=2.10(5)$, $beta=0.47(2)$, in relatively good agreement with the Bethe ansatz prediction $z=2$. From a mean-field continuum formulation, a characteristic relaxation time, related to kinematic-wave propagation and having an effective exponent $z^prime=1$, is shown to be the limiting slow process for the low density phase, which accounts for the above-mentioned discrepancy with Bethe ansatz results. For TASEP with quenched bond disorder, interface width scaling gives $alpha=1.05(5)$, $z=1.7(1)$, $beta=0.62(7)$. From a direct analytic approach to steady-state properties of TASEP with quenched disorder, closed-form expressions for the piecewise shape of averaged density profiles are given, as well as rather restrictive bounds on currents. All these are substantiated in numerical simulations.
We study numerically the non-equilibrium critical properties of the Ising model defined on direct products of graphs, obtained from factor graphs without phase transition (Tc = 0). On this class of product graphs, the Ising model features a finite temperature phase transition, and we find a pattern of scaling behaviors analogous to the one known on regular lattices: Observables take a scaling form in terms of a function L(t) of time, with the meaning of a growing length inside which a coherent fractal structure, the critical state, is progressively formed. Computing universal quantities, such as the critical exponents and the limiting fluctuation-dissipation ratio X_infty, allows us to comment on the possibility to extend universality concepts to the critical behavior on inhomogeneous substrates.
We introduce a model of interacting lattices at different resolutions driven by the two-dimensional Ising dynamics with a nearest-neighbor interaction. We study this model both with tools borrowed from equilibrium statistical mechanics as well as non-equilibrium thermodynamics. Our findings show that this model keeps the signature of the equilibrium phase transition. Moreover the critical temperature of the equilibrium models correspond to the state maximizing the entropy and delimits two out-of-equilibrium regimes, one satisfying the Onsager relations for systems close to equilibrium and one resembling convective turbulent states. Since the model preserves the entropy and energy fluxes in the scale space, it seems a good candidate for parametric studies of out-of-equilibrium turbulent systems.
Driven lattice gases as the ASEP are useful tools for the modeling of various stochastic transport processes carried out by self-driven particles, such as molecular motors or vehicles in road traffic. Often these processes take place in one-dimensional systems offering several tracks to the particles, and in many cases the particles are able to change track with a given rate. In this work we consider the case of strong coupling where the hopping rate along the tracks and the exchange rates are of the same order, and show how a phenomenological approach based on a domain wall theory can describe the dynamics of the system. In particular, the domain walls on the different tracks form pairs, whose dynamics dominate the behavior of the system.
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