The XY Model on a Dynamical Random Lattice

TL;DR

This paper investigates the XY model on a dynamically fluctuating lattice, providing numerical evidence for its phase structure and critical behavior, and connecting it to theories involving 2D quantum gravity.

Contribution

It offers the first detailed numerical analysis of the XY model on a fluctuating lattice, supporting analytical predictions of its phase structure and critical exponents.

Findings

Strong support for the two-phase structure predicted analytically.

Finite size scaling yields estimates for critical exponents.

Topological features are crucial in understanding the system's behavior.

Abstract

We study the XY model on a lattice with fluctuating connectivity. The expectation is that at an appropriate critical point such a system corresponds to a compactified boson coupled to 2d quantum gravity. Our simulations focus, in particular, on the important topological features of the system. The results lend strong support to the two phase structure predicted on the basis of analytical calculations. A careful finite size scaling analysis yields estimates for the critical exponents in the low temperature phase.