Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

Abstract

We consider models with nearest-neighbor interactions and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\ge 1$. It is known that the "splitting Gibbs measures" of the model can be described by solutions of a nonlinear integral equation. For arbitrary $k\ge 2$ we find a sufficient condition under which the integral equation has unique solution, hence under the condition the corresponding model has unique splitting Gibbs measure.

arXiv comment13 pages

References in corpus (2)

• Non-uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree
• No phase transition for Gaussian fields with bounded spins

Cited by in corpus (3)

• Periodic Gibbs Measures for Models with Uncountable Set of Spin Values on a Cayley Tree
• On the positive fixed points of quartic operators
• Non-translation-invariant Gibbs Measures for Models With Uncountable Set of Spin Values on a Cayley Tree