Universality in the two-dimensional dilute Baxter-Wu model

Abstract

We study the question of universality in the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field ∆. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of ∆ and a parallelized variant of the multicanonical approach performed at constant temperature T . A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (∆, T ) phase diagram indicates that the transition belongs to the universality class of the 4-state Potts model. Previous controversies with respect to the nature of the transition are discussed and possibly attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.

Multiple transitions in an infinite range p-spin random-crystal field Blume Capel model

“…We expect a similar study for p ≥ 3 p-spin model would also result in new ordered states and rich phase diagram. A study of the model on a triangular lattice to look for the possibility of multiple transitions in finite dimensions would also be interesting [17][18][19]. and q in terms of m and H via Eq.…”

“…where r and ∆ are the bias of the distribution and the strength of the random-crystal field respectively. The r = 0 and 1 corresponds to the dilute BW model for p = 3 [16][17][18][19]. We consider ∆ > 0 and 0 ≤ r ≤ 1 throughout this paper.…”

“…[15]. The spin-1 BW model with pure crystal field has attracted a lot of recent attention [16][17][18][19]. In this paper we report the behaviour of the pRCBCM for any p ≥ 3, including the p → ∞ limit, for bimodal and Gaussian distributions of the random-crystal field on a fully connected graph.…”