Non-uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

Details Non-uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree Non-uniqueness of Gibbs Measure for Models With Uncountable Set of Spin Values on a Cayley Tree

2012-02-12

arxiv.org/abs/1202.2542v1

Mathematics

Functional Analysis

16 pages

Scientific paper

In this paper we construct several models with nearest-neighbor interactions
and with the set $[0,1]$ of spin values, on a Cayley tree of order $k\geq 2$.
We prove that each of the constructed model has at least two
translational-invariant Gibbs measures.

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