Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain

Abstract

The one-dimensional Ising model is easily generalized to a \textit{genuinely nonequilibrium} system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system. In particular, we obtain the evolution of the magnetisation, starting with arbitrary initial conditions. For slightly less general initial conditions, we compute the time dependence of all correlation functions, and so, the probability distribution. Novel properties, such as oscillatory decays into the steady state, are presented. Finally, we comment on the relationship to a reaction-diffusion model with pair annihilation and creation.

Submitted to J. Phys. A (Letter to the editor)

References in corpus (4)

• Stationary correlations for a far-from-equilibrium spin chain
• Exact solution of a class of one-dimensional nonequilibrium stochastic models
• Non-equilibrium stationary state of a two-temperature spin chain
• Exact multipoint and multitime correlation functions of a one-dimensional model of adsorption and evaporation of dimers

Cited by in corpus (13)

• Probability currents as principal characteristics in the statistical mechanics of non-equilibrium steady states
• Master equations and the theory of stochastic path integrals
• Non-equilibrium statistical mechanics of a two-temperature Ising ring with conserved dynamics
• Exact dynamics of a reaction-diffusion model with spatially alternating rates
• Energy flux near the junction of two Ising chains at different temperatures
• Exact energy spectrum of a two-temperature kinetic Ising model
• Dynamical phase transition in one-dimensional kinetic Ising model with nonuniform coupling constants
• Glauber's Ising chain between two thermostats
• Thermal contact through a two-temperature kinetic Ising chain
• New family of symmetric orthogonal polynomials and a solvable model of a kinetic spin chain
• Nonuniform autonomous one-dimensional exclusion nearest-neighbor reaction-diffusion models
• One-dimensional kinetic Ising model with nonuniform coupling constants
• Nonuniform autonomous one-dimensional exclusion nearest neighbor reaction diffusion models, II