Three Dimensional Quantum Gravity Coupled to Ising Matter

TL;DR

This paper maps the phase diagram of 3D quantum gravity coupled with Ising matter, revealing the absence of disordered phases in negative curvature and identifying two spin phases with a first order transition in positive curvature.

Contribution

It provides the first detailed analysis of phase behavior in 3D quantum gravity coupled to Ising matter, highlighting curvature-dependent phase structures.

Findings

No disordered phase in negative curvature due to diverging site coordination.

Existence of two distinct spin phases in positive curvature.

First order transition observed between the spin phases.

Abstract

We establish the phase diagram of three--dimensional quantum gravity coupled to Ising matter. We find that in the negative curvature phase of the quantum gravity there is no disordered phase for ferromagnetic Ising matter because the coordination number of the sites diverges. In the positive curvature phase of the quantum gravity there is evidence for two spin phases with a first order transition between them.