Exact solution for an Ising model on the Cayley tree of order 5

Abstract

Abstract.We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order 5. The translation Gibbs measures is considered for this model. Our result of the critical curve shows that the phase transition occurs in this model, further it confirms a particular case of a conjecture.

Gibbs measures of an Ising-Vannimenus Model with one-level competing interactions on 4th order Cayley tree

“…Gibbs measure and infinite random systems were introduced in 's by Dobrushin who introduced the Markov random fields on the d-dimensional lattices [ 1 ]. During the last few decades many authors dealt with the problem of Gibbs measures and phase transitions [ [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] ].…”