Changeover phenomenon in randomly colored Potts models

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 mean field (MF) all-to-all. Exact expressions for the second order critical line in concentration-temperature parameter space of the MF model together with some other related critical properties, are derived.