Phase transitions with four-spin interactions

TL;DR

This paper proves the conditions under which ferromagnetic multi-spin interactions exhibit phase transitions and spontaneous magnetization, using advanced mathematical inequalities, and also discusses the absence of such transitions in some nonferromagnetic cases.

Contribution

It extends the Lee-Yang theorem and GKS inequalities to analyze phase transitions in multi-spin interactions, broadening the understanding of ferromagnetic and nonferromagnetic systems.

Findings

Ferromagnetic multi-spin interactions have phase transitions at zero external field and low temperatures.

Nonferromagnetic interactions can lack phase transitions under certain conditions.

FKG inequalities apply to a broader class of multi-spin interactions.

Abstract

Using an extended Lee-Yang theorem and GKS correlation inequalities, we prove, for a class of ferromagnetic multi-spin interactions, that they will have a phase transition(and spontaneous magnetization) if, and only if, the external field $h=0$ (and the temperature is low enough). We also show the absence of phase transitions for some nonferromagnetic interactions. The FKG inequalities are shown to hold for a larger class of multi-spin interactions.