Renormalization group at criticality and complete analyticity of constrained models: A numerical study |
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Authors: | Emilio N M Cirillo Enzo Olivieri |
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Institution: | (1) Dipartimento di Fisica dell'Università di Bari and Istituto Nazionale di Fisica Nucleare, Sezione di Bari, I-70126 Bari, Italy;(2) Dipartimento di Matematica, II Università di Roma Tor Vergata, 00173 Rome, Italy |
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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 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 2D case, complete analyticity from which, as 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 the DSU condition is verified for a large enough volumeV for all constrained models. |
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Keywords: | Majority rule renormalization group non-Gibbsianness finite-size conditions complete analyticity Ising model |
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