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- Title
Periodic Gibbs measures for models with uncountable set of spin values on a Cayley tree.
- Authors
Rozikov, U. A.; Haydarov, F. H.
- Abstract
We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k ≥ 1. We show that periodic Gibbs measures are either translation-invariant or periodic with period two. We describe two-periodic Gibbs measures of the model. For k = 1 we show that there is no any periodic Gibbs measure. In case k ≥ 2 we get a sufficient condition on Hamiltonian of the model with uncountable set of spin values under which the model has no periodic Gibbs measure. We construct several models which have at least two periodic Gibbs measures.
- Subjects
GIBBS' equation; MEASURE theory; SET theory; SPIN valves; CAYLEY graphs; TREE graphs
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2015, Vol 18, Issue 1, p-1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S021902571550006X