Critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field

Abstract

The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.

An entropic simulational study of the spin-$1$ Baxter-Wu model in a crystal field

“…5, we show the phase diagram. The continuous line represents the tetracritical points that separate the 1.3089 1.2225 Dias [3] 0.890254 1.1690 Our results 1.68288(62) 0.98030 (10) TABLE I. Comparison of our results for the pentacritical point to those obtained by Costa [2] and Dias [3].…”

“…The spin-1 Baxter-Wu (BW) model in a crystal field [1][2][3] is a generalization of the original spin− 1 2 BW model [4][5][6][7], which includes a crystal field anisotropic term D, in addition to the three-spin interaction. The Hamiltonian of the model considered here is…”

“…The existence of a pentacritical point was conjectured at D c = 1.3089 and T c = 1.2225. Recently, Dias et al [3] by applying finitesize scaling and conformal invariance, analyzed both the spin-1 and spin-3/2 cases. For the latter, they extended the size of the strips that are used in reference [2] and found D c = 0.890254 and T c = 1.1690.…”

Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems

“…The decomposition of this tetracritical point into a critical endpoint with 2-phase coexistence (see Figure 2 g) and another tricritical point, as depicted in the inset (2) of Figure 5 b, is also permitted by the generalized GPR. Although both situations above are spurious and do not happen in the global phase diagram of this system [ 28 , 29 ], such decomposition has actually been seen in the spin-3/2 Baxter–Wu model [ 19 ].…”

“…Figure 2 gives examples for , , and , which makes it easy to generalize for cases of more than four phases (see, for instance, ref. [ 19 ] for cases with five and eight phases). In general, if we originally have coexisting phases, we can say that: ( i ) if only two phases become identical, one has a critical endpoint with -phase coexistence ( is a critical end point and is a critical point); ( ii ) if only three phases become identical, one has a tricritical endpoint with -phase coexistence ( is a tricritical end point and is a tricritical point); ( iii ) and so on for tetra, penta, etc.…”