Energy Transport in an Ising Disordered Model

Details Energy Transport in an Ising Disordered Model Energy Transport in an Ising Disordered Model

2009-07-27

arxiv.org/abs/0907.4623v1

J. Stat. Mech. (2009) P07041

Physics

Condensed Matter

Statistical Mechanics

14 pages, 8 figures

Scientific paper

10.1088/1742-5468/2009/07/P07041

We introduce a new microcanonical dynamics for a large class of Ising systems isolated or maintained out of equilibrium by contact with thermostats at different temperatures. Such a dynamics is very general and can be used in a wide range of situations, including disordered and topologically inhomogenous systems. Focusing on the two-dimensional ferromagnetic case, we show that the equilibrium temperature is naturally defined, and it can be consistently extended as a local temperature when far from equilibrium. This holds for homogeneous as well as for disordered systems. In particular, we will consider a system characterized by ferromagnetic random couplings $J_{ij} \in [ 1 - \epsilon, 1 + \epsilon ]$. We show that the dynamics relaxes to steady states, and that heat transport can be described on the average by means of a Fourier equation. The presence of disorder reduces the conductivity, the effect being especially appreciable for low temperatures. We finally discuss a possible singular behaviour arising for small disorder, i.e. in the limit $\epsilon \to 0$.

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