Changeover phenomenon in randomly colored Potts models

Abstract

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* 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.

Potts model with invisible states on a scale-free network

“…It was shown that the model exhibits a first-order phase transition when the number of "molecule states" is high [25]. An interesting is the case of a hybrid Potts model [26]. Within 𝑞 𝑐 states, it introduces two subsets of states, that can be occupied with different probability.…”