Abstract
Two-dimensional generalized XY spin model on a triangular lattice is studied by means of Monte-Carlo simulations. The critical temperatures of Berezinskii-Kosterlitz-Thouless (BKT) phase transition are obtained by the method of helicity modulus. It is found that the results are consistent with those obtained by other methods. The vortex density and the vortex-antivortex pair formation energy are also obtained. The result shows that the critical temperature decreases with the increase of the generalization parameter q. While the vortex-antivortex pair formation energy increases with the increase of q when q>1.
Highlights
The critical phase transition behavior of two-dimensional spin models has been the subject of intense study in recent years
The simulations were performed on a triangular lattice with periodic boundary conditions for system size N L × L, where the largest size of lattice is considered as L 80
We mainly focus on discussion of vortex density and helicity modulus in the case of different q
Summary
The critical phase transition behavior of two-dimensional spin models has been the subject of intense study in recent years. The two-dimensional (2D) XY spin model is one of the most intensively studied due to it’s a paradigmatic example of phase transitions mediated by topological defects [1–4]. Vortices and Helicity Modulus corresponds to the usual XY model and the case q 0 is the planar rotator model with two-component spins. In this model, an ordering transition taking place at finite temperature for 3D is supported by mean field and two-site cluster approaches [14]. Vortex density and the vortex-antivortex pair formation energy have an extremely important reference for the study of BKT phase transition. We further expand research content and discuss in detail the vortex density and helicity modulus
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