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One-dimensional random-field ising model: Gibbs states and structure of ground states (1996)

Bleher, P. M. ; Ruiz, J. ; Zagrebnov, V. A.

Springer

Journal of statistical physics 84 (1996), S. 1077-1093

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ISSN: 1572-9613

Keywords: Gibbs states ; ground states ; residual entropy ; random field ; Ising model

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract We consider the random Gibbs field formalism for the ferromagnetic ID dichotomous random-field Ising model as the simplest example of a quenched disordered system. We prove that for nonzero temperatures the Gibb state is unique for any realization of the external field. Then we prove that asT→0, the Gibbs state converges to a limit, a ground state, for almost all realizations of the external field. The ground state turns out to be a probability measure concentrated on an infinite set of configurations, and we give a constructive description of this measure.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02174129

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