New insight into the Berezinskii-Kosterlitz-Thouless phase transition

14th Mexican Workshop on Particles and Fields

Gerber, Urs^1 ; Bietenholz, Wolfgang^1 ; Rejón-Barrera, Fernando G.^2

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal

C.P. 04510, Mexico^1

Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Postbus 94485, Amsterdam

1090 GL, Netherlands^2

关键词: Anti vortices;    Continuum limits;    Helicity modulus;    Important features;    Kosterlitz-Thouless phase transition;    Perturbation theory;    Scaling behavior;    Second orders;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/651/1/012010/pdf
DOI  :  10.1088/1742-6596/651/1/012010

来源: IOP

【 摘 要 】

We investigate the 2d XY model by using the constraint angle action, which belongs to the class of topological lattice actions. These actions violate important features usually demanded for a lattice action, such as the correct classical continuum limit and the applicability of perturbation theory. Nevertheless, they still lead to the same universal quantum continuum limit and show excellent scaling behavior. By using the constraint angle action we gain new insight into the Berezinskii-Kosterlitz-Thouless phase transition of the 2d XY model. This phase transition is of special interest since it is one of the few examples of a phase transition beyond second order. It is of infinite order and therefore an essential phase transition. In particular, we observe an excellent scaling behavior of the helicity modulus, which characterizes this phase transition. We also observe that the mechanism of (un)binding vortex-anti-vortex pairs follows the usual pattern, although free vortices do not require any energy in the formulation of the 2d XY model using the constraint angle action.