Critical behavior of mean-field XY and related models

TL;DR

This paper analyzes the critical behavior and phase transitions of mean-field XY and related spin models on complete graphs, using large deviations and Stein's method to derive limit theorems and convergence rates.

Contribution

It introduces new theoretical results on phase transitions and limit theorems for mean-field XY models and related systems, employing advanced probabilistic techniques.

Findings

Characterization of phase transition behavior

Limit theorems with convergence rates

Application of large deviations and Stein's method

Abstract

We discuss spin models on complete graphs in the mean-field (infinite-vertex) limit, especially the classical XY model, the Toy model of the Higgs sector, and related generalizations. We present a number of results coming from the theory of large deviations and Stein's method, in particular, Cram\'er and Sanov-type results, limit theorems with rates of convergence, and phase transition behavior for these models.