Existence of Algebraic Decay in Nonabelian Ferromagnets

TL;DR

This paper demonstrates that nonabelian two-dimensional ferromagnets exhibit algebraic decay of correlations at low temperatures, extending known results from abelian models using novel ergodicity methods.

Contribution

It introduces a new approach to analyze nonabelian ferromagnets by mapping them to site-bond percolation and employing ergodicity, establishing algebraic decay in models with continuous symmetry.

Findings

All ferromagnets with continuous symmetry show algebraic decay at low temperatures.

The method involves mapping to site-bond percolation processes.

A novel ergodicity approach is used to analyze correlation decay.

Abstract

The low temperature regime of nonabelian two-dimensional ferromagnets is investigated. The method involves mapping such models into certain site-bond peroclation processes and using ergodicity in a novel fashion. It is concluded that all ferromagnets possessing a continuous symmetry (abelian or not) exihibit algebraic decay of correlations at sufficiently low temperatures.