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.
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Conrady, F. Space as a Low-Temperature Regime of Graphs. J Stat Phys 142, 898–917 (2011). https://doi.org/10.1007/s10955-011-0135-9
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DOI: https://doi.org/10.1007/s10955-011-0135-9