Changeover phenomenon in randomly colored Potts models

Abstract

A hybrid Potts model where a random concentration p of the spins assume q0 states and a random concentration 1−p of the spins assume q > q0 states is introduced. It is known that when the system is homogeneous, with an integer spin number q0 or q, it undergoes a second or a first order transition, respectively. It is argued that there is a concentration p * such that the transition nature of the model is changed at p * . This idea is demonstrated analytically and by simulations for two different types of interaction: the usual square lattice nearest neighboring and the mean field all-to-all interaction. Exact expressions for the second order critical line in concentration-temperature parameter space of the mean field model together with some other related critical properties, are derived.