Perturbation expansion for the diluted two-dimensional XY model

TL;DR

This paper develops a perturbation expansion method to analyze the quasi-long-range order in a diluted 2D XY model, showing good agreement with Monte Carlo simulations across various dilution levels.

Contribution

It introduces a third-order perturbation expansion approach to study the effects of quenched site-dilution on the 2D XY model's ordered phase.

Findings

Expansion results agree with Monte Carlo data

Effective for dilution levels far from percolation threshold

Provides insights into the effects of quenched disorder

Abstract

We study the quasi-long-range ordered phase of a 2D XY model with quenched site-dilution using the spin-wave approximation and expansion in the parameter which characterizes the deviation from completely homogeneous dilution. The results, obtained by keeping the terms up to the third order in the expansion, show good accordance with Monte Carlo data in a wide range of dilution concentrations far enough from the percolation threshold. We discuss different types of expansion.