Phase transitions with four-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.

Cited by in corpus (5)

• Some Applications of the Lee-Yang Theorem
• Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
• On cluster properties of classical ferromagnets in an external magnetic field
• Central limit theorems, Lee-Yang zeros, and graph-counting polynomials
• Graph-counting polynomials for oriented graphs