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

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

2010-08-30

arxiv.org/abs/1008.5099v1

Europhysics Letters (EPL) 91 (2010) 50003

Physics

Condensed Matter

Statistical Mechanics

6 pages, 4 figures, submitted to EPL

Scientific paper

10.1209/0295-5075/91/50003

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 $T'=\infty$ 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 $T\rightarrow 0$, this decay crosses over to a power law ($x^{-3}$) and resembles a "critical" system. Simulations affirm our analytic results.

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