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Renormalization Group Transformations under strong mixing conditions: gibbsianess and convergence of renormalized interactions

L. Bertini·E. N. M. Cirillo·E. Olivieri
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Abstract

In this paper we study a renormalization-group map: the block averaging transformation applied to Gibbs measures relative to a class of finite range lattice gases, when suitable strong mixing conditions are satisfied. Using block decimation procedure, cluster expansion (like in [HK]) and detailed comparison between statistical ensembles, we are able to prove Gibbsianess and convergence to a trivial (i.e. Gaussian and product) fixed point. Our results apply to 2D standard Ising model at any temperature above the critical one and arbitrary magnetic field.

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L. Bertini, E. N. M. Cirillo, E. Olivieri. 1999-05-31. Renormalization Group Transformations under strong mixing conditions: gibbsianess and convergence of renormalized interactions. https://doi.org/10.1023/a%3A1004620929047

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