Renormalization Group Transformations under strong mixing conditions: gibbsianess and convergence of renormalized interactions
Statistical Mechanics
2015-06-25 v1
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.
Cite
@article{arxiv.cond-mat/9905434,
title = {Renormalization Group Transformations under strong mixing conditions: gibbsianess and convergence of renormalized interactions},
author = {L. Bertini and E. N. M. Cirillo and E. Olivieri},
journal= {arXiv preprint arXiv:cond-mat/9905434},
year = {2015}
}
Comments
Plain TeX, 68 pages, 10 PostScript figures