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- Title
Description of weakly periodic Gibbs measures for the isingmodel on a cayley tree.
- Authors
Rozikov, U.; Rakhmatullaev, M.
- Abstract
We introduce the concept of a weakly periodic Gibbs measure. For the Ising model, we describe a set of such measures corresponding to normal subgroups of indices two and four in the group representation of a Cayley tree. In particular, we prove that for a Cayley tree of order four, there exist critical values T c < T cr of the temperature T > 0 such that there exist five weakly periodic Gibbs measures for 0 < T < T c or T > T cr , three weakly periodic Gibbs measures for T = T c , and one weakly periodic Gibbs measure for T c < T ≤ T cr .
- Subjects
ISING model; CAYLEY algebras; REPRESENTATIONS of groups (Algebra); NONASSOCIATIVE algebras; MATHEMATICS
- Publication
Theoretical & Mathematical Physics, 2008, Vol 156, Issue 2, p1218
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1007/s11232-008-0091-y