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 ∣φ x ∣ ⩽m/2. The main result is that for β⩾β0, where β0 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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Mazel, A.E., Suhov, Y.M. Random surfaces with two-sided constraints: An application of the theory of dominant ground states. J Stat Phys 64, 111–134 (1991). https://doi.org/10.1007/BF01057870
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DOI: https://doi.org/10.1007/BF01057870