On phase transition and vortex stability in the generalized XY models

Abstract

We study a recent generalization proposed for the XY model in two and three dimensions. Using both, the continuum limit and discrete lattice, we obtained the vortex configuration and shown that out-of-plane vortex solutions are deeply jeopardized whenever the parameter of generalization, L, is increased. The critical temperature for such models is calculated using the self consistent harmonic approximation. In both, two-and three-dimensional cases, such a temperature decreases with raising L. Our results are also compared with other approximated methods available in the literature.

Berezinskii–Kosterlitz–Thouless phase transition of 2D dilute generalized model

“…In turn, different techniques, such as self-consistent harmonic approximation (SCHA) and Monte Carlo (MC) simulation, have been used to study this transition when q > 1. It was found that the BKT critical temperature decreases as q increases and this model was proved to be the same universality class as the usual XY model [7,9,10,8]. Once the BKT transition appears, the vortex pair density starts to grow simultaneously.…”

First-order transitions for some generalizedXYmodels

“…In some recent papers [8,24,25,27] a class of generalized XY models was introduced and studied. These models are ferromagnetic and, in the simplest case, restricted to a nearestneighbour XY -type interaction.…”

Numerical Studies of Vortices and Helicity Modulus in the Two-Dimensional Generalized XY Model

“…When q is small, the first-order phase transition phenomenon is not obvious, or even there may be no first-order phenomenon. When q is large enough, such as q > 6, the first-order phase transition becomes more and more obvious [14][15][16][17]. We know that the BKT phase transition is caused by the release of vortex antivortex pairs at the critical temperature point.…”

“…As shown in Figure 4, the vortex density increases almost precipitously with the increase of q. These two kinds of phase transitions occur at almost the same temperature point, so it is difficult to accurately judge the phase transition properties [15,16]. How to accurately determine the first-order phase transition temperature may be an interesting research in the future.…”

“…In turn, different techniques, such as self-consistent harmonic approximation (SCHA) and Monte Carlo (MC) simulation, had been used to investigate this transition for all values of q. It is found that the phase transition temperature of this phase transition decreases with the increase of q, and it is confirmed that this second-order phase transition is similar to XY type, that is, it belongs to BKT type phase transition [15][16][17]. Using Monte Carlo simulation, some physical quantities such as vortex density, specific heat, energy and critical temperature are obtained on different lattices [15,18].…”