L. Bertini et al., Renormalization-group transformations under strong mixing conditions: Gibbsianness and convergence of renormalized interactions, J STAT PHYS, 97(5-6), 1999, pp. 831-915
In this paper we study a renormalization-group map: the block averaging tra
nsformation applied to Gibbs measures relative to a class of finite-range l
attice gases, when suitable strong mixing conditions are satisfied. Using a
block decimation procedure, cluster expansion. and detailed comparison bet
ween statistical ensembles, we are able to prove Gibbsianness and convergen
ce to a trivial (i.e., Gaussian and product) fixed point. Our results apply
to the 2D standard Ising model dr any temperature above the critical one a
nd arbitrary magnetic field.