Energy flux near the junction of two Ising chains at different temperatures

Abstract

We consider a system in a non-equilibrium steady state by joining two semi-infinite Ising chains coupled to thermal reservoirs with {\em different} temperatures, $T$ and $T^{\prime }$. To compute the energy flux from the hot bath through our system into the cold bath, we exploit Glauber heat-bath dynamics to derive an exact equation for the two-spin correlations, which we solve for $T^{\prime }=\infty$ and arbitrary $T$. We find that, in the $T^{\prime }=\infty$ sector, the in-flux occurs only at the first spin. In the $T<\infty$ sector (sites $x=1,2,...$), the out-flux shows a non-trivial profile: $F(x)$. Far from the junction of the two chains, $F(x)$ decays as $e^{-x/\xi }$, where $\xi$ is twice the correlation length of the {\em equilibrium} Ising chain. As $T\to 0$, this decay crosses over to a power law ($x^{-3}$) and resembles a "critical" system. Simulations affirm our analytic results.

6 pages, 4 figures, submitted to EPL

References in corpus (2)

• Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain
• Injected Power Fluctuations in 1D Dissipative Systems

Cited by in corpus (2)

• Non-equilibrium statistical mechanics of a two-temperature Ising ring with conserved dynamics
• Stochastic Two-temperature Nonequilibrium Ising model