AUTHOR=Sun Yun-Zhou , Wu Qin , Yang Xiao-Li , Zhou Yan , Zhu Lan-Yan , Chen Quan , An Qing 

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

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.851322

DOI=10.3389/fphy.2022.851322

ISSN=2296-424X

ABSTRACT=<p>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 <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math></inline-formula>. While the vortex-antivortex pair formation energy increases with the increase of <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math></inline-formula> when <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>q</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></inline-formula>.</p>