Random surfaces with two-sided constraints: An application of the theory of dominant ground states |
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| Authors: | A. E. Mazel Yu. M. Suhov |
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| Affiliation: | (1) International Institute of Earthquake Prediction Theory and Mathematical Geophysics, USSR Academy of Sciences, 113556 Moscow, USSR;(2) Institute for Problems of Information Transmission, USSR Academy of Sciences, GSP-4, 101447 Moscow, USSR;(3) Statistical Laboratory, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, CB2 1SB Cambridge, England, UK |
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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   x  m/2. The main result is that for   0, where 0 does not depend onm, the structure of thermodynamic phases in the model is determined by dominant ground states: for an evenm a Gibbs state is unique and for an oddm the number of space-periodic pure Gibbs states is two. |
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| Keywords: | Random surfaces SOS model with symmetric constraints dominant ground states |
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