Ising model on Cayley trees: a new class of Gibbs measures and their comparison with known ones

2017/05/15 by Rakhmatullaev, M. M., Rozikov, U. A.
#60K35 #82B26 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1705.05184

Abstract

For the Ising model on Cayley trees we give a very wide class of new Gibbs measures. We show that these new measures are extreme under some conditions on the temperature. We give a review of all known Gibbs measures of the Ising model on trees and compare them with our new measures.

Related

• The Potts model on a Cayley tree: the new class of Gibbs measures
• On new weakly periodic Gibbs measures of Ising model on a Cayley tree
• Gibbs-non-Gibbs properties for evolving Ising models on trees
• Almost Gibbsian Measures on a Cayley Tree
• Gibbs measures and free energies of the Ising-Vannimenus Model on the Cayley tree