Bulk and surface properties in the critical phase of the two-dimensional XY model

TL;DR

This study uses Monte Carlo simulations and conformal mappings to analyze bulk and surface critical properties of the 2D XY model, revealing how correlation exponents vary with temperature in the critical phase.

Contribution

It introduces a method combining Monte Carlo simulations with conformal mappings to determine temperature-dependent correlation exponents in the 2D XY model.

Findings

Determined the bulk correlation exponent η_σ(T) as a function of temperature.

Measured the surface correlation exponent η_||(T) across the critical phase.

Provided insights into the boundary effects in the 2D XY model.

Abstract

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with various boundary conditions (BC). Using conformal mappings we deduce the exponent $\eta_\sigma(T)$ of the order parameter correlation function and its surface analogue $\eta_\|(T)$ as a function of the temperature in the critical (low-temperature) phase of the model.