Quantum gravity and spin systems

TL;DR

This paper introduces a novel approach to quantum gravity using spin systems to approximate the simplicial path integral, enabling easier analysis and revealing similarities to established models in different dimensions.

Contribution

It presents a new nonperturbative method for quantum gravity based on spin systems, bridging simplicial path integrals and statistical models.

Findings

Equivalence to an Ising model with ternary couplings in 2D

Simulations in 4D show phase structure similar to Regge theory

Method simplifies analytical and numerical studies of quantum gravity

Abstract

A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations considerably. In two dimensions equivalence to an Ising model with ternary couplings is recovered. First simulations in four dimensions indicate strong similarities to the phase structure of original Regge theory.