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Energy flux near the junction of two Ising chains at different temperatures
- Source :
- Europhysics Letters (EPL) 91 (2010) 50003
- Publication Year :
- 2010
-
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 $T'=\infty$ 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.<br />Comment: 6 pages, 4 figures, submitted to EPL
- Subjects :
- Condensed Matter - Statistical Mechanics
Subjects
Details
- Database :
- arXiv
- Journal :
- Europhysics Letters (EPL) 91 (2010) 50003
- Publication Type :
- Report
- Accession number :
- edsarx.1008.5099
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1209/0295-5075/91/50003