We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Four competing interactions for models with an uncountable set of spin values on a Cayley tree.
- Authors
Rozikov, U.; Haydarov, F.
- Abstract
We consider models with four competing interactions ( external field, nearest neighbor, second neighbor, and three neighbors) and an uncountable set [0, 1] of spin values on the Cayley tree of order two. We reduce the problem of describing the splitting Gibbs measures of the model to the problem of analyzing solutions of a nonlinear integral equation and study some particular cases for Ising and Potts models. We also show that periodic Gibbs measures for the given models either are translation invariant or have the period two. We present examples where periodic Gibbs measures with the period two are not unique.
- Subjects
CAYLEY graphs; GIBBS' equation; ISING model; POTTS model; PHASE transitions
- Publication
Theoretical & Mathematical Physics, 2017, Vol 191, Issue 3, p910
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1134/S0040577917060095