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Nonequilibrium Quantum Phase Transitions in the Ising Model  [PDF]
V. M. Bastidas,C. Emary,G. Schaller,T. Brandes
Physics , 2012, DOI: 10.1103/PhysRevA.86.063627
Abstract: We establish a set of nonequilibrium quantum phase transitions in the Ising model driven under monochromatic nonadiabatic modulation of the transverse field. We show that besides the Ising-like critical behavior, the system exhibits an anisotropic transition which is absent in equilibrium. The nonequilibrium quantum phases correspond to states which are synchronized with the external control in the long-time dynamics.
Nonequilibrium Stationary States of Harmonic Chains with Bulk Noises  [PDF]
Cedric Bernardin,Venkateshan Kannan,Joel L. Lebowitz,Jani Lukkarinen
Mathematics , 2011, DOI: 10.1140/epjb/e2011-20746-0
Abstract: We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites 1 and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.
Hysteretic nonequilibrium Ising-Bloch transition  [PDF]
V. B. Taranenko,A. Esteban-Martin,G. J. de Valcarcel,E. Roldan
Physics , 2005, DOI: 10.1103/PhysRevE.73.027201
Abstract: We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this pheomenon [A. Esteban-Martin et al., Phys. Rev. Lett. 94, 223903 (2005)].
Deterministic Derivation of NonEquilibrium Free Energy Theorems for Natural Isothermal Isobaric Systems  [PDF]
Stephen R. Williams,Debra J. Searles,Denis J. Evans
Physics , 2006, DOI: 10.1080/00268970701278393
Abstract: The nonequilibrium free energy theorems show how distributions of work along nonequilibrium paths are related to free energy differences between the equilibrium states at the end points of these paths. In this paper we develop a natural way of barostatting a system and give the first deterministic derivation of the Crooks and Jarzynski relations for these isothermal isobaric systems. We illustrate these relations by applying them to molecular dynamics simulations of a model polymer undergoing stretching.
Coarsening Dynamics of Nonequilibrium Chiral Ising Models  [PDF]
Mina Kim,Su-Chan Park,Jae Dong Noh
Physics , 2012, DOI: 10.1103/PhysRevE.87.012129
Abstract: We investigate a nonequilibrium coarsening dynamics of a one-dimensional Ising spin system with chirality. Only spins at domain boundaries are updated so that the model undergoes a coarsening to either of equivalent absorbing states with all spins + or -. Chirality is imposed by assigning different transition rates to events at down (+-) kinks and up (-+) kinks. The coarsening is characterized by power-law scalings of the kink density $\rho \sim t^{-\delta}$ and the characteristic length scale $\xi \sim t^{1/z}$ with time $t$. Surprisingly the scaling exponents vary continuously with model parameters, which is not the case for systems without chirality. These results are obtained from extensive Monte Carlo simulations and spectral analyses of the time evolution operator. Our study uncovers the novel universality class of the coarsening dynamics with chirality.
Block renormalization study on the nonequilibrium chiral Ising model  [PDF]
Mina Kim,Su-Chan Park,Jae Dong Noh
Statistics , 2014, DOI: 10.1103/PhysRevE.91.012132
Abstract: We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of $+-$ spins can flip to $++$ or $--$ with probability $(1-u)$ or to $-+$ with probability $u$ while $-+$ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any $u<1$ exhibiting the power-law scaling of the characteristic length scale $\xi\sim t^{1/z}$ and the domain wall density $\rho\sim t^{-\delta}$. The scaling exponents $z$ and $\delta$ were found to vary continuously with the parameter $u$. In order to establish the anomalous power-law scaling firmly, we perform the block spin renormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech. (2011) P11023]. Domain walls of $b$ sites are coarse-grained into a block spin $\sigma^b$, and the relative frequencies of two-block patterns $\sigma^b_1 \sigma^b_2$ are measured in the $b\to\infty$ and $t\to\infty$ limit. These indices are expected to be universal. By performing extensive Monte Carlo simulations, we find that the indices also vary continuously with $u$ and that their values are consistent with the scaling exponents found in the previous study. This study serves as another evidence for the claim that the nonequilibrium chiral Ising model displays the power-law scaling behavior with continuously varying exponents.
The Dynamics of Nonequilibrium Transitions Induced By the Cross-Correlated Noises: Numerical Results  [PDF]
A.N. Vitrenko,I.A. Knyaz’,V.S. Budeniy,D.O. Lytvynenko
Journal of Nano- and Electronic Physics , 2010,
Abstract: The dynamic system described by the Langevin equation with two cross-correlated Gaussian white noises is considered. The non-equilibrium probability distribution function of the system is calculated by the numerical methods. The time of change of the initially unimodal distribution to the bimodal one is determined for different values of the control parameter. A critical slowing down in the transition dynamics is demonstrated.
Local scale invariance in the parity conserving nonequilibrium kinetic Ising model  [PDF]
Geza Odor
Statistics , 2006, DOI: 10.1088/1742-5468/2006/11/L11002
Abstract: The local scale invariance has been investigated in the nonequilibrium kinetic Ising model exhibiting absorbing phase transition of PC type in 1+1 dimension. Numerical evidence has been found for the satisfaction of this symmetry and estimates for the critical ageing exponents are given.
Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models  [PDF]
Francisco Sastre,Ivan Dornic,Hugues Chaté
Physics , 2003, DOI: 10.1103/PhysRevLett.91.267205
Abstract: We show that a nominal temperature can be consistently and uniquely defined everywhere in the phase diagram of large classes of nonequilibrium kinetic Ising spin models. In addition, we confirm the recent proposal that, at critical points, the large-time ``fluctuation-dissipation ratio'' $X_\infty$ is a universal amplitude ratio and find in particular $X_\infty \approx 0.33(2)$ and $X_\infty = 1/2$ for the magnetization in, respectively, the two-dimensional Ising and voter universality classes.
Nonequilibrium wetting transition in a nonthermal 2D Ising model  [PDF]
Jef Hooyberghs,Joseph O. Indekeu
Physics , 2011, DOI: 10.1140/epjb/e2011-20085-2
Abstract: Nonequilibrium wetting transitions are observed in Monte Carlo simulations of a kinetic spin system in the absence of a detailed balance condition with respect to an energy functional. A nonthermal model is proposed starting from a two-dimensional Ising spin lattice at zero temperature with two boundaries subject to opposing surface fields. Local spin excitations are only allowed by absorbing an energy quantum (photon) below a cutoff energy E_c. Local spin relaxation takes place by emitting a photon which leaves the lattice. Using Monte Carlo simulation nonequilibrium critical wetting transitions are observed as well as nonequilibrium first-order wetting phenomena, respectively in the absence or presence of absorbing states of the spin system. The transitions are identified from the behavior of the probability distribution of a suitably chosen order parameter that was proven useful for studying wetting in the (thermal) Ising model.
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