The XY Model Coupled to Two-Dimensional Quantum Gravity

TL;DR

This paper investigates the XY model's phase transition behavior when coupled to two-dimensional quantum gravity through Monte Carlo simulations, comparing results with theoretical expectations and exploring universality properties.

Contribution

It provides the first numerical analysis of the XY model on dynamical gravity graphs, confirming the KT transition persists and examining universality with Potts models at c=1.

Findings

KT transition remains when coupled to gravity

Universality with Potts models extends to XY model

Numerical results match theoretical predictions

Abstract

We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we discovered in our earlier work on various Potts models with the same value of the central charge, $c$, carries over to the XY model, which has $c=1$.