Graduate Thesis Or Dissertation
 

Aggregate Path Coupling for the Generalized Curie-Weiss Model

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  • The topic of statistical mechanics has been studied for over a century, and it is one of the pillars of modern physics. This theory can be applied to the study of the thermodynamic behavior of large systems of interacting particles, in which case it is referred to as equilibrium statistical mechanics. In this branch, the goal is to derive results about the statistical equilibrium of a system, given its temperature and the rules for the interaction of its particles. In this dissertation, we focus on the generalized Curie-Weiss model, introduced by T. Eisele and R. Ellis in 1988, as well as its equilibrium states, phase transitions, and mixing times. Different from most other works in the literature, this model allows the spin set to be uncountable. Furthermore, it has different phase transitions (first-order and second-order) at different critical temperatures. These properties of the generalized Curie-Weiss model require developing novel techniques that enable the analysis of its Glauber dynamics. In this work, we modify the aggregate path coupling method and successfully apply it for computing the mixing times of the stochastic dynamics.
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