Chiral perturbation theory, finite size effects and the three-dimensional $XY$ model

TL;DR

This paper investigates finite size effects in the three-dimensional XY model using chiral perturbation theory, calculating key physical quantities through Monte Carlo simulations and analyzing the validity of theoretical expansions.

Contribution

It introduces a method to determine physical quantities from finite size effects in the 3D XY model using chiral perturbation theory and Monte Carlo simulations.

Findings

Magnetization and helicity modulus depend on two low energy constants.

Finite size effects can be accurately described to order (1/L)^2.

The validity range of the theoretical expansions is analyzed.

Abstract

We study finite size effects of the d=3 $XY$ model in terms of the chiral perturbation theory. We calculate by Monte Carlo simulations physical quantities which are, to order of $(1/L)^2$, uniquely determined only by two low energy constants. They are the magnetization and the helicity modulus (or the Goldstone boson decay constant) in infinite volume. We also pay a special attention to the region of the validity of the two possible expansions in the theory.