Gibbsian Properties and Convergence of the Iterates for the Block Averaging Transformation

#### L. Bertini, E.N.M. Cirillo, E. Olivieri

2004, v.10, Issue 3, 381-394

ABSTRACT

We analyze the Block Averaging Transformation applied to the two-dimensional Ising model in the uniqueness region. We discuss the Gibbs property of the renormalized measure and the convergence of renormalized potential under iteration of the map. It turns out that for any temperature $T$ higher than the critical one $T_c$ the renormalized measure is strongly Gibbsian, whereas for $TT_c$ and in a weak sense for $T$.

Keywords: lattice systems,cluster expansion,disordered systems,renormalization group