Potts Model with Invisible States: A Review

TL;DR

This review discusses the Potts model with invisible states, highlighting how adding non-interacting states affects phase transition order and entropy, with implications for various physical systems.

Contribution

It provides a comprehensive overview of the Potts model with invisible states, summarizing its theoretical foundations, effects on phase transitions, and applications in physics.

Findings

Invisible states alter phase transition order from second to first.

The model explains discrepancies between theory and experiments.

It has broad applications in physical systems.

Abstract

The Potts model with invisible states was introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where $Z_q$ symmetry is spontaneously broken. It differs from the ordinary $q$-state Potts model in that each spin, besides the usual $q$ visible states, can be also in any of $r$ so-called invisible states. Spins in an invisible state do not interact with their neighbours but they do contribute to the entropy of the system. As a consequence, an increase in $r$ may cause a phase transition to change from second to first order. Potts models with invisible states describe a number of systems of interest in physics and beyond and have been treated by various tools of statistical and mathematical physics. In this paper we aim to give a review of this fundamental topic.