Space as a low-temperature regime of graphs

TL;DR

This paper introduces a statistical graph model where 2D surfaces emerge at low temperatures, revealing a phase transition between surface-forming and disordered regimes through simulations and observable analysis.

Contribution

It presents a novel graph-based model demonstrating the emergence of 2D surfaces at low temperature and analyzes the phase transition with respect to topology and defects.

Findings

Surface configurations form triangulations at low temperature

A phase transition occurs between surface and non-surface regimes

Observable data suggest a possible phase transition

Abstract

I define a statistical model of graphs in which 2-dimensional spaces arise at low temperature. The configurations are given by graphs with a fixed number of edges and the Hamiltonian is a simple, local function of the graphs. Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear. I use data for the specific heat and other observables to discuss whether this is a phase transition. The surface states are analyzed with regard to topology and defects.