Statistical Mechanics of Graphity Models

TL;DR

This paper investigates the statistical mechanics of graphity models, analyzing their phase behavior through analytical and numerical methods, and highlights the importance of matter in forming extended geometric structures at low temperatures.

Contribution

It provides new analytical and numerical insights into the phase transitions and geometric properties of graphity models, emphasizing the role of matter degrees of freedom.

Findings

High- and low-temperature behaviors characterized

Transitions between different graph phases analyzed

Matter degrees of freedom are crucial for extended geometries

Abstract

Graphity models are characterized by configuration spaces in which states correspond to graphs and Hamiltonians that depend on local properties of graphs such as the degrees of vertices and numbers of short cycles. As statistical systems, graphity models can be studied analytically by estimating their partition functions or numerically by Monte Carlo simulations. Results presented here are based on both of these approaches and give new information about the high- and low-temperature behavior of the models and the transitions between them. In particular, it is shown that matter degrees of freedom must play an important role in order for the low-temperature regime to be described by graphs resembling interesting extended geometries.