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 Jij ∈ [1−_,1+_]. 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 _ → 0.
Energy transport in an Ising disorderedmodel / Agliari, Elena; Casartelli, Mario; Vezzani, Alessandro. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - P07041:(2009), pp. 1-15. [10.1088/1742-5468/2009/07/P07041]
Energy transport in an Ising disorderedmodel
AGLIARI, Elena;CASARTELLI, Mario;VEZZANI, Alessandro
2009-01-01
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 Jij ∈ [1−_,1+_]. 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 _ → 0.File | Dimensione | Formato | |
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