Monte Carlo Study of the Phase Transition of the $XY$ Model on a Diamond Lattice

TL;DR

This paper investigates the phase transition of the classical XY model on a diamond lattice using Monte Carlo simulations, confirming its universality class and precise critical parameters.

Contribution

It provides a detailed Monte Carlo analysis of the XY model on a diamond lattice, accurately determining critical temperature and exponents.

Findings

Critical temperature T_c = 1.30036(1)

Correlation length exponent ν = 0.671(6)

Confirms 3D XY universality class

Abstract

We study the phase transition of the classical $XY$ model on a diamond lattice by Monte Carlo simulations using the Wolff cluster algorithm. Finite-size scaling (FSS) analysis of the Binder cumulant and the second-moment correlation length ratio $\xi_{2\rm nd}/L$ yields $T_c = 1.30036(1)$ and $\nu = 0.671(6)$. Data collapse of both quantities confirms the three-dimensional $XY$ universality class.