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

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.

Plain TeX, 68 pages, 10 PostScript figures

References in corpus (3)

• Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
• Renormalization-group at criticality and complete analyticity of constrained models: a numerical study
• Some Numerical Results on the Block Spin Transformation for the 2D Ising Model at the Critical Point

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• Relative entropy, Gaussian concentration and uniqueness of equilibrium states
• Gibbsian properties and convergence of the iterates for the Block Averaging Transformation
• Coarse-graining schemes for stochastic lattice systems with short and long-range interactions.