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CORRELATIONS IN A NONEQUILIBRIUM STEADY STATE: EXACT RESULTS FOR A GENERALIZED KINETIC

Michael Plischke, British Columbia, Canadá

Published Jan 1, 1987• 0 citations
OpenAlex

Abstract

A one-dimensional kinetic Ising model with domain wall dynamics corresponding to diffusion-limited annihilation in the presence of particle sources is considered. The spin-spin correlation function C, is calculated exactly for a nonequilibrium steady state which can be brought close to a critical point of the system. We find that in contrast to equilibrium situations, C, contains two distinctly diverging correlation lengths ~ ~ ~ 42, where ~2 is a length closely related to the nonequilibrium kinetics of the system.

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A one-dimensional kinetic Ising model with domain wall dynamics corresponding to diffusion-limited annihilation in the presence of particle sources is considered. The spin-spin correlation function C, is calculated exactly for a nonequilibrium steady state which can be brought close to a critical point of the system. We find that in contrast to equilibrium situations, C, contains two distinctly diverging correlation lengths ~ ~ ~ 42, where ~2 is a length closely related to the nonequilibrium kinetics of the system.
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Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and Kawasaki-type spin-exchange kinetics at infinite temperature T are investigated here in one dimension from the point of view of phase transition and critical behaviour. Branching annihilating random walks with an even number of offspring (on the part of the ferromagnetic domain boundaries), is a decisive process in forming the steady state of the system for a range of parameters, in the family of models considered. A wide variety of quantities characterize the critical behaviour of the system. Results of computer simulations and of a generalized mean field theory are presented and discussed.
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Investigates the bicritical dynamics of one-dimensional bond-diluted kinetic Ising models in the percolation limit at criticality. A wide class of single-spin-flip dynamics is applied and domain boundary diffusion arguments are used to identify the dominant processes producing flipping of the ordered finite chain segments constituting the diluted chain. Exact expressions for the rate of flip as a function of length of segment are obtained and are used to derive corresponding expressions for the decay of equilibrium correlations, and of the magnetisation (from a non-equilibrium uniformly magnetised initial state) in the chain. The results are in agreement with those of earlier rigorous calculations restricted to the special case of Glauber dynamics.
In the limit of the strong magnetic field , the closed hierarchy of kinetic equations for correlation functions of an arbitrary order is derived for a one-dimensional kinetic Ising model. This hierarchy allows asymptotically exact solution in quadratures. For the first time the closed set of equation for generating functions of the domain distribution of the identically oriented spins have been obtained. The relations between kinetic parameters that make it possible to find exact solutions in quadratures are indicated.
The kinetic Glauber–Ising spin chain is one of the very few exactly solvable models of non-equilibrium statistical mechanics. Nevertheless, existing solutions do not yield tractable expressions for two-time correlation and response functions of observables involving products of more than one or two spins. We use a new approach to solve explicitly the full hierarchy of differential equations for the correlation and response functions. From this general solution follow closed expressions for arbitrary multispin two-time correlation and response functions, for the case where the system is quenched from equilibrium at T i > 0 to some arbitrary T ⩾ 0. By way of application, we give the results for two- and four-spin two-time correlation and response functions. From the standard mapping, these also imply new exact results for two-time particle correlation and response functions in one-dimensional diffusion limited annihilation.