 9674 Emilio N. M. Cirillo, Enzo Olivieri
 RenormalizationGroup at Criticality and Complete Analyticity of
Constrained Models: a Numerical Study.
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Mar 14, 96

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Abstract. We study the majority rule transformation applied to the Gibbs measure for the
2D 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 DobrushinShlosman Uniqueness
(DSU) finitesize condition for the "constrained models" corresponding to
different configurations of the "image" system. It is known that DSU implies,
in our 2D 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.
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