The F model on dynamical quadrangulations

TL;DR

This paper explores the critical behavior of the 6-vertex F model coupled with dynamical quadrangulations in two-dimensional quantum gravity, using Monte Carlo simulations to analyze critical exponents and phase transitions.

Contribution

It introduces a new approach by using quadrangles instead of triangles in dynamical triangulations and adapts Monte Carlo algorithms for this setting.

Findings

Determined critical exponents for the coupled model.

Identified phase transition characteristics.

Validated the use of quadrangulations in quantum gravity simulations.

Abstract

The dynamically triangulated random surface (DTRS) approach to Euclidean quantum gravity in two dimensions is considered for the case of the elemental building blocks being quadrangles instead of the usually used triangles. The well-known algorithmic tools for treating dynamical triangulations in a Monte Carlo simulation are adapted to the problem of these dynamical quadrangulations. The thus defined ensemble of 4-valent graphs is appropriate for coupling to it the 6- and 8-vertex models of statistical mechanics. Using a series of extensive Monte Carlo simulations and accompanying finite-size scaling analyses, we investigate the critical behaviour of the 6-vertex F model coupled to the ensemble of dynamical quadrangulations and determine the matter related as well as the graph related critical exponents of the model.