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

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

1999-05-31

arxiv.org/abs/cond-mat/9905434v1

Journ. Stat. Phys. 97, 831-915 (1999)

Physics

Condensed Matter

Statistical Mechanics

Plain TeX, 68 pages, 10 PostScript figures

Scientific paper

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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