First-order transitions for n-vector models in two and more dimensions; rigorous proof

TL;DR

This paper rigorously proves that a class of n-vector models with specific interaction properties undergo first-order phase transitions in two or more dimensions, regardless of their low-temperature phase characteristics.

Contribution

It provides a rigorous mathematical proof of first-order transitions for SO(n)-invariant n-vector models with deep, narrow minima in their interactions in dimensions two and higher.

Findings

First-order transitions occur in these models in two or more dimensions.

The transition is independent of the nature of the low-temperature phase.

The proof applies to models with interactions having a deep and narrow minimum.

Abstract

We prove that various SO(n)-invariant n-vector models with interactions which have a deep and narrow enough minimum have a first-order transition in the temperature. The result holds in dimension two or more, and is independent on the nature of the low-temperature phase.