Finite-size scaling analysis of the two-dimensional 3-state and 4-state Potts and clock models using Wolff cluster simulations

Abstract

This study examines the universality between two-dimensional models, namely the 3-state Potts and 3-state clock model, along with the 4-state Potts and 4-state clock model, using the Wolff cluster algorithm, Markov chain Monte Carlo simulations of different square lattice sizes. While it is known that higher-q clock models behave differently and that the 3-state Potts and clock models are conceptually equivalent, there is still little systematic finite-size scaling comparison between the two models using the Wolff cluster method. This study clarifies the importance of symmetry and interaction structure in defining critical behavior by using the Wolff algorithm inside a unified framework to provide a direct numerical comparison that illustrates both the expected universality at q = 3 and its breakdown at q = 4. These are done by applying the finite-size scaling analysis of the susceptibility peaks to determine the ratio of the critical exponents, and then the universality of the 3-state and 4-state of each model through a data collapse. The results highlight the likely possibility that the 3-state Potts and clock models are indeed in the same universality class since their critical exponents and data collapse agree with each other. Also, the results obtained for the 4-state Potts and clock models expressed the difference between these two models for q = 4. These observations give insights into the universality and scaling relations of two different models for two different values of q.