Bertini L., Cirillo E.N.M., Olivieri E.
Renormalization Group Transformations under strong mixing conditions: 
gibbsianess and convergence of renormalized interactions
(124K, TeX Plain)

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 {\it at any} temperature above the critical
one  and arbitrary magnetic field.