On Phase Transition and Vortex Stability in the Generalized XY Models

TL;DR

This paper investigates how a generalization of the XY model affects vortex stability and phase transition temperatures in two and three dimensions, revealing that increased generalization parameter L destabilizes vortices and lowers critical temperatures.

Contribution

It provides a detailed analysis of vortex configurations and phase transition temperatures in the generalized XY model across dimensions, highlighting the impact of the parameter L.

Findings

Out-of-plane vortex solutions are destabilized as L increases.

Critical temperature decreases with increasing L in both 2D and 3D.

Results are compared with existing approximation methods.

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.