RENORMALIZATION-GROUP AT CRITICALITY AND COMPLETE ANALYTICITY OF CONSTRAINED MODELS - A NUMERICAL STUDY

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 re normalized measure is Gibbsian. We analyze the validity of Dobrushin-S hlosman uniqueness (DSU) finite-size condition for the ''constrained m odels'' corresponding to different configurations of the ''image'' sys tem. Ii is known that DSU implies, in our 2D case, complete analyticit y from which, as recently shown by Haller and Kennedy, Gibbsianness Fo llows. 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 the DSU condition is verified for a large enough volume V for all constrained models.