3d quantum gravity coupled to matter

TL;DR

This paper explores the phase structure of three-dimensional quantum gravity coupled with an Ising model using numerical simulations, revealing weak coupling away from criticality and persistent first-order transitions.

Contribution

It provides the first numerical investigation of matter coupling in 3D quantum gravity with Ising spins, analyzing phase transitions and coupling effects.

Findings

Weak coupling between matter and geometry away from critical point

Clear matter-geometry coupling at criticality

Persistence of first-order phase transition in quantum gravity

Abstract

We investigate the phase structure of three-dimensional quantum gravity coupled to an Ising spin system by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial manifolds, and the Ising spins are located in the center of the tetrahedra, which constitute the building blocks of the piecewise linear manifold. We find that the coupling between spin and geometry is weak away from the critical point of the Ising model. At the critical point there is clear coupling, which however does not seem to change the first order transition between the ``hot'' and ``cold'' phase of three dimensional simplicial quantum gravity observed earlier.