Artículos de revistas
Phase Transition for the Ising Model on the Critical Lorentzian Triangulation
Date
2012Registration in:
JOURNAL OF STATISTICAL PHYSICS, NEW YORK, v. 148, n. 3, pp. 422-439, AUG, 2012
0022-4715
10.1007/s10955-012-0548-0
Author
Krikun, Maxim
Yambartsev, Anatoly
Institutions
Abstract
The ferromagnetic 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 the Peierls contour method. The critical temperature is shown to be constant a.s.