Abstract
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 $\Delta \gtrsim 0$.
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 language | English |
|---|---|
| Article number | 024140 |
| Number of pages | 11 |
| Journal | Physical Review E |
| Volume | 108 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 25 Aug 2023 |