A generalization of the spherical model: Reentrant phase transition in the spin one ferromagnet

TL;DR

This paper maps the spin one ferromagnet onto the spherical model to explore phase transitions, revealing a reentrant ferromagnetic-paramagnetic transition in three dimensions, unlike in lower dimensions.

Contribution

It introduces a novel mapping approach to analyze phase transitions in spin one ferromagnets, uncovering reentrant behavior in three dimensions.

Findings

No phase transition in 1D and 2D

Reentrant ferromagnetic-paramagnetic transition in 3D

Phase diagram with unexpected low-temperature transition

Abstract

By mapping the hamiltonian of the spin one ferromagnet onto that of the classical spherical model we investigate the possible phase transitions and the phase diagram of the spin one ferromagnet. Similarly to what happens in the spherical model we find no phase transition in one and two dimensions. Nonetheless, for three dimensions we obtain a phase diagram in which the most important and unexpected feature is the existence of a ferromagnetic-paramagnetic transition at low temperatures.