Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-03-14
Journ. Stat. Phys. 86, (1997)
Physics
High Energy Physics
High Energy Physics - Theory
39 pages, teX file, 4 Postscript figures, 1 TeX figure
Scientific paper
10.1007/BF02183617
We study the majority rule transformation applied to the Gibbs measure for the 2--D Ising model at the critical point. The aim is to show that the renormalized hamiltonian is well defined in the sense that the renormalized measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman Uniqueness (DSU) finite-size condition for the "constrained models" corresponding to different configurations of the "image" system. It is known that DSU implies, in our 2--D case, complete analyticity from which, as it has been recently shown by Haller and Kennedy, Gibbsianness follows. We introduce a Monte Carlo algorithm to compute an upper bound to Vasserstein distance (appearing in DSU) between finite volume Gibbs measures with different boundary conditions. We get strong numerical evidence that indeed DSU condition is verified for a large enough volume $V$ for all constrained models.
Cirillo Emilio N. M.
Olivieri Emiliano
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