Steady-state properties of coupled hot and cold Ising chains

Abstract

Recently, the author and Zia (2010) reported on exact results for a far-from-equilibrium system in which two coupled semi-infinite Ising chains at temperatures $T_h$ and $T_c$, with $T_h>T_c$, establish a flux of energy across their junction. This paper provides a complete derivation of those results, more explicit expressions for the energy flux, and a more detailed characterization of the system at arbitrary $T_c$ and $T_h$. We consider the two-point correlation functions and the energy flux $F(x)$ between each spin, located at integer position $x$, and its associated heat bath. In the $T_h\to \infty$ limit, the flux $F(x)$ decays exponentially into the cold bath (spins with $x=1,2,...$) for all $T_c>0$ and transitions into a power law decay as $T_c\to 0$. We find an asymptotic expansion for large $x$ in terms of modified Bessel functions that captures both of these behaviors. We perform Monte Carlo simulations that give excellent agreement with both the exact and asymptotic results for $F(x)$. The simulations are also used to study the system at arbitrary $T_h$ and $T_c$.

27 pages, 8 figures, submitted to J. Phys. A

References in corpus (3)

• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Injected Power Fluctuations in 1D Dissipative Systems
• Exact dynamics of a reaction-diffusion model with spatially alternating rates

Cited by in corpus (5)

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• Phase diagram and specific heat of a nonequilibrium Curie-Weiss model
• Glauber's Ising chain between two thermostats
• Thermal contact through a two-temperature kinetic Ising chain
• Stochastic Two-temperature Nonequilibrium Ising model