Order-disorder on cluster dynamics in the Q2R-Potts cellular automaton

Cellular automata (CA) are mathematical models that allow the study of emergent behavior from a bottom-up point of view, while the Potts model is renowned for its rich dynamics capable of developing both first and second order phase transitions. Here, we study the Q2R-Potts cellular automaton, which is a model that merges cellular automata and the Potts model through a microcanonical ensemble characterized by a conservative energy-like function. Our study, conducted via numerical simulations, focuses on the one-dimensional Q2R-Potts CA with three (q = 3) states, examining its dynamics through both macroscopic and microscopic quantities. We discover that the model exhibits a first-order phase transition from order to disorder around of a critical energy density, characterized by a discontinuity in a phase diagram and self-organizing clusters that follow a power-law behavior.