Two-dimensional dilute Baxter-Wu model: Transition order and universality

• Main Authors: Macedo, A. R. S, Vasilopoulos, A, Akritidis, M, Plascak, J. A, Fytas, N. G, Weigel, M
• Format: Journal Article
• Language: English
• Published: 07-08-2023
• Subjects: Physics - Statistical Mechanics
• DOI: 10.48550/arxiv.2304.12379

Phys. Rev. E 108, 024140 (2023) We investigate the critical behavior of the two-dimensional spin-$1$
Baxter-Wu model in the presence of a crystal-field coupling $\Delta$ with the
goal of determining the universality class of transitions along the
second-order part of the transition line as one approaches the putative
location of the multicritical point. We employ extensive Monte Carlo
simulations using two different methodologies: (i) a study of the zeros of the
energy probability distribution, closely related to the Fisher zeros of the
partition function, and (ii) the well-established multicanonical approach
employed to study the probability distribution of the crystal-field energy. A
detailed finite-size scaling analysis in the regime of second-order phase
transitions in the $(\Delta, T)$ phase diagram supports previous claims that
the transition belongs to the universality class of the $4$-state Potts model.
For positive values of $\Delta$, we observe the presence of strong finite-size
effects, indicative of crossover effects due to the proximity of the
first-order part of the transition line. Finally, we demonstrate how a
combination of cluster and heat-bath updates allows one to equilibrate larger
systems, and we demonstrate the potential of this approach for resolving the
ambiguities observed in the regime of $\Delta \gtrsim 0$.