Space as a low-temperature regime of graphs

Details Space as a low-temperature regime of graphs Space as a low-temperature regime of graphs

2010-09-16

arxiv.org/abs/1009.3195v3

J.Statist.Phys.142:898,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, 12 figures; v3: published version; J.Stat.Phys. 2011

Scientific paper

10.1007/s10955-011-0135-9

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.

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