The Potts model with invisible states was introduced to explain discrepancies between theoretical predictions and experimental observations of phase transitions in some systems where Zq 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.

M. Krasnytska, P. Sarkanych, B. Berche, Y. Holovatch, R. Kenna, Potts model with invisible states: a review, The European Physical Journal Special Topics (2023) DOI: 10.1140/epjs/s11734-023-00843-3.