Discrete gravity from statistical mechanics

TL;DR

This paper establishes a novel connection between discrete gravity and statistical mechanics, enabling the calculation of the quantum wave function of the universe using models like Ising and Potts, and deriving Regge equations from statistical principles.

Contribution

It introduces a method to construct spacetime lattices with Regge actions linked to statistical models, bridging quantum gravity and statistical mechanics.

Findings

Constructed spacetime lattices from Ising and Potts models

Derived Regge equations using statistical mechanics principles

Proposed a new approach to quantum gravity calculations

Abstract

We show how to construct space time lattices with a Regge action proportional to the energy of a given Ising or Potts model macrostate. This allows to take advantage of the existence of exact solutions for these models to calculate the quantum wave function of the universe using the sum over the histories approach to quantum gravity. Motivated by this isomorphism we show how the Regge equations, i.e. the discrete equivalent of the vacuum Einstein equations, can be derived using statistical mechanics under the assumption that the energy of a given space time geometry is proportional to the Regge action.