Changeover phenomenon in randomly colored Potts models

A hybrid Potts model where a random concentration \(p\) of the spins assume \(q_0\) states and a random concentration \(1-p\) of the spins assume \(q>q_0\) states is introduced. It is known that when the system is homogeneous, with an integer spin number \(q_0\) or \(q\), it undergoes a second or a first order transition, respectively. It is argued that there is a concentration \(p^\ast\) such that the transition nature of the model is changed at \(p^\ast\). This idea is demonstrated analytically and by simulations for two different types of interaction: the usual square lattice nearest neighboring and mean field all-to-all. 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.