ON GRADIENT GIBBS MEASURES WITH 4-PERIODIC BOUNDARY LAWS OF MODEL OF SOS TYPE ON THE CAYLEY TREE OF ORDER TWO AND THREE
Keywords:
Generalized SOS model, specification, potential, hamiltonian, boundary law, spin values, Cayley tree, gradient Gibbs measure. Mathematics Subject Classification (2010):Abstract
We consider Gradient Gibbs measures corresponding to a periodic boundary law for a generalized SOS model with spin values from a countable set, on Cayley trees. On the Cayley tree, detailed information on Gradient Gibbs measures for models of SOS model are given in [3, 8, 11, 16]. Investigating these works for the generalized SOS model, in this paper the problem of finding Gradient Gibbs measures which correspond to periodic boundary laws is reduced to a functional equation.
By solving this equation all Gradient Gibbs measures with 4 periodic boundary laws are found.
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