Random surfaces with two-sided constraints: An application of the theory of dominant ground states

A. E. Mazel; Yu M. Suhov

doi:10.1007/BF01057870

Random surfaces with two-sided constraints: An application of the theory of dominant ground states

A. E. Mazel, Yu M. Suhov

Mathematics

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Abstract

We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints {divides}φ_x{divides} ≤m/2. The main result is that for β≥β₀, where β₀ does not depend on m, the structure of thermodynamic phases in the model is determined by dominant ground states: for an even m a Gibbs state is unique and for an odd m the number of space-periodic pure Gibbs states is two.

Original language	English (US)
Pages (from-to)	111-134
Number of pages	24
Journal	Journal of Statistical Physics
Volume	64
Issue number	1-2
DOIs	https://doi.org/10.1007/BF01057870
State	Published - Jul 1991

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints {divides}φx{divides} ≤m/2. The main result is that for β≥β0, where β0 does not depend on m, the structure of thermodynamic phases in the model is determined by dominant ground states: for an even m a Gibbs state is unique and for an odd m the number of space-periodic pure Gibbs states is two.",

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AB - We consider some models of classical statistical mechanics which admit an investigation by means of the theory of dominant ground states. Our models are related to the Gibbs ensemble for the multidimensional SOS model with symmetric constraints {divides}φx{divides} ≤m/2. The main result is that for β≥β0, where β0 does not depend on m, the structure of thermodynamic phases in the model is determined by dominant ground states: for an even m a Gibbs state is unique and for an odd m the number of space-periodic pure Gibbs states is two.

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Random surfaces with two-sided constraints: An application of the theory of dominant ground states

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