Statistical Mechanics of Graphity Models

Details Statistical Mechanics of Graphity Models Statistical Mechanics of Graphity Models

2008-05-15

arxiv.org/abs/0805.2283v2

Phys.Rev.D78:044032,2008

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 8 figures; v2. minor changes

Scientific paper

10.1103/PhysRevD.78.044032

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.

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