Surface properties at the Kosterlitz-Thouless transition

TL;DR

This study uses Monte Carlo simulations and conformal mapping to accurately determine bulk and surface critical exponents at the Kosterlitz-Thouless transition in the 2D XY model, even for small systems.

Contribution

It introduces a conformal mapping approach to precisely extract surface and bulk exponents at the KT transition from finite-size simulations.

Findings

Bulk exponent eta(T_{KT}) = 1/4 confirmed

Surface exponent eta_parallel(T_{KT}) approximately 0.54

Shape effects are effectively incorporated in the conformal mapping

Abstract

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent eta of the order parameter correlation function and its surface equivalent eta_parallel at the Kosterlitz-Thouless transition temperature. The well known value eta(T_{KT}) = 1/4 is easily recovered even with systems of relatively small sizes, since the shape effects are encoded in the conformal mapping. The exponent associated to the surface correlations is similarly obtained eta_1(T_{KT}) ~= 0.54.