Absence of phase transitions in a class of integer spin systems

TL;DR

This paper demonstrates that certain integer spin systems, including those with infinite-range interactions and the Blume-Emery-Griffiths model in disordered phases, lack phase transitions due to their free energy's convergent series representation.

Contribution

It establishes the absence of phase transitions in a broad class of integer spin systems with specific interaction decay properties and disordered phases.

Findings

Free energy expressed as an absolutely convergent series at all temperatures.

Includes spin systems with polynomially decaying infinite-range interactions.

Applies to the disordered phase of the Blume-Emery-Griffiths model.

Abstract

We exhibit a class of integer spin systems whose free energy can be written in term of an absolutely convergent series at any temperature. This class includes spin systems on $\Z^d$ interacting through infinite range pair potential polynomially decaying at large distances $r$ at a rate $1/r^{d+\e}$ with $\e>0$. It also contains the Blume-Emery-Griffiths model in the disordered phase at large values of the crystal field.