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

Arilton Macedo, Alexandros Vasilopoulos, Michail Akritidis, Joao Plascak , Nikos Fytas, Martin Weigel

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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 $\Delta \gtrsim 0$.
Original languageEnglish
Article number024140
Number of pages11
JournalPhysical Review E
Issue number2
Publication statusPublished - 25 Aug 2023

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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.


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