Phase transition for the Ising model on the Critical Lorentzian triangulation

Details Phase transition for the Ising model on the Critical Lorentzian triangulation Phase transition for the Ising model on the Critical Lorentzian triangulation

2008-10-13

arxiv.org/abs/0810.2182v1

Mathematics

Probability

Scientific paper

Ising model without external field on an infinite Lorentzian triangulation sampled from the uniform distribution is considered. We prove uniqueness of the Gibbs measure in the high temperature region and coexistence of at least two Gibbs measures at low temperature. The proofs are based on the disagreement percolation method and on a variant of Peierls method. The critical temperature is shown to be constant a.s.

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