Phase Transition in the Two Dimensional Classical XY Model

TL;DR

This paper presents extensive high-temperature phase data for the 2D XY model using a novel finite size scaling Monte Carlo method, confirming some theoretical predictions but also revealing inconsistencies with established RG results.

Contribution

It introduces a new finite size scaling Monte Carlo technique and provides detailed data near criticality for the 2D XY model.

Findings

Verification that η=1/4 near criticality

Clarification of correction to scaling behavior

Inconsistency with standard FSS analysis predictions

Abstract

For the two dimensional classical XY model we present extensive high -temperature -phase bulk data extracted based on a novel finite size scaling (FSS) Monte Carlo technique, along with FSS data near criticality. Our data verify that $\eta=1/4$ sets in near criticality, and clarify the nature of correction to the leading scaling behavior. However, the result of standard FSS analysis near criticality is inconsistent with other predictions of Kosterlitz's renormalization group approach.