Ising Model Coupled to Three-Dimensional Quantum Gravity

TL;DR

This paper presents Monte Carlo simulations of the Ising model coupled to 3D quantum gravity, exploring phase transitions and the effects of different spin placements on the triangulation.

Contribution

It introduces a novel simulation approach for the Ising model on dynamical triangulations coupled to quantum gravity, comparing vertex and dual placements of spins.

Findings

Observed likely second-order phase transitions.

Dual spin placement couples more effectively to quantum gravity.

Simulations performed in microcanonical and grand canonical ensembles.

Abstract

We have performed Monte Carlo simulations of the Ising model coupled to three-dimensional quantum gravity based on a summation over dynamical triangulations. These were done both in the microcanonical ensemble, with the number of points in the triangulation and the number of Ising spins fixed, and in the grand canoncal ensemble. We have investigated the two possible cases of the spins living on the vertices of the triangulation (``diect'' case) and the spins living in the middle of the tetrahedra (``dual'' case). We observed phase transitions which are probably second order, and found that the dual implementation more effectively couples the spins to the quantum gravity.