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 ones with disordered and topologically inhomogeneous systems. Focusing on the two-dimensional ferromagnetic case, we show that the equilibrium temperature is naturally defined, and that 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 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 .

Energy transport in an Ising disordered model / Agliari, E; Casartelli, M; Vezzani, A. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - ELETTRONICO. - 2009:07(2009), p. P07041. [10.1088/1742-5468/2009/07/P07041]

Energy transport in an Ising disordered model

Agliari, E;
2009

Abstract

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 ones with disordered and topologically inhomogeneous systems. Focusing on the two-dimensional ferromagnetic case, we show that the equilibrium temperature is naturally defined, and that 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 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 .
2009
transport processes/heat transfer (theory); disordered systems (theory); heat conduction
01 Pubblicazione su rivista::01a Articolo in rivista
Energy transport in an Ising disordered model / Agliari, E; Casartelli, M; Vezzani, A. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - ELETTRONICO. - 2009:07(2009), p. P07041. [10.1088/1742-5468/2009/07/P07041]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1100421
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