Abstract:
This dissertation investigates Gibbs and non-Gibbs measures for Potts and Ewens models defined on Cayley trees. Special attention is paid to models with a countable set of spin values and to the influence of the tree structure on the existence, uniqueness, and classification of Gibbs measures. Translation-invariant and periodic Gibbs measures for the Potts model with competing interactions are described, and explicit exponential solutions of the corresponding boundary law equations are obtained. Furthermore, multivariate Ewens probability distributions on regular trees are studied, and it is rigorously proved that these distributions are non-Gibbsian. The results contribute to the theory of Gibbs measures on non-amenable graphs and provide new explicit examples of non-Gibbsian behavior beyond renormalization-based constructions.
Website:
https://us06web.zoom.us/j/3836418273
|
