On the stochastic dynamics of Ising models |
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Authors: | Ph. A. Martin |
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Affiliation: | (1) Laboratoire de Physique Théorique, Ecole Polytechnique Fédérale, Lausanne, Switzerland |
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Abstract: | With the help of recent results in the mathematical theory of master equations, we present a rigorous derivation of the stochastic Glauber dynamics of Ising models from Hamiltonian quantum mechanics. A thermal bath is explicitly constructed and, as an illustration, the dynamics of the Ising-Weiss model is analyzed in the thermodynamic limit. We thus obtain an example of a nonequilibrium statistical mechanical system for which a link without mathematical gap can be established from microscopic quantum mechanics to a macroscopic irreversible thermodynamic process. |
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Keywords: | Stochastic dynamics Ising model thermal bath master equation Markov process nonequilibrium thermodynamics |
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