Ising-link Quantum Gravity

TL;DR

This paper introduces a simplified Ising-link model of quantum gravity on a lattice, analyzing its phase transition behavior and comparing it to traditional Regge quantum gravity.

Contribution

It proposes a binary link-length quantum gravity model and investigates its critical behavior through numerical simulations, highlighting differences from continuous Regge theory.

Findings

Peak in curvature susceptibility indicating a phase transition

Critical exponent differs from continuous Regge theory

Behavior of curvature at transition is distinct from prior models

Abstract

We define a simplified version of Regge quantum gravity where the link lengths can take on only two possible values, both always compatible with the triangle inequalities. This is therefore equivalent to a model of Ising spins living on the links of a regular lattice with somewhat complicated, yet local interactions. The measure corresponds to the natural sum over all 2^links configurations, and numerical simulations can be efficiently implemented by means of look-up tables. In three dimensions we find a peak in the ``curvature susceptibility'' which grows with increasing system size. However, the value of the corresponding critical exponent as well as the behavior of the curvature at the transition differ from that found by Hamber and Williams for the Regge theory with continuously varying link lengths.