Energy flux near the junction of two Ising chains at different temperatures
Department of Physics, Harvard University - Cambridge, MA 02138-2933, USA
2 Department of Physics, Virginia Tech - Blacksburg, VA 24061-0435, USA
Accepted: 26 August 2010
We consider a system in a non-equilibrium steady state by joining two semi-infinite Ising chains coupled to thermal reservoirs with different temperatures, T and T′. 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′ = ∞ and arbitrary T. We find that, in the T′ = ∞ sector, the in-flux occurs only at the first spin. In the T < ∞ 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/ξ, where ξ is twice the correlation length of the equilibrium Ising chain. As T → 0, this decay crosses over to a power law (x−3) and resembles a “critical” system. Simulations affirm our analytic results.
PACS: 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.70.Ln – Nonequilibrium and irreversible thermodynamics
© EPLA, 2010