Gibbsian properties and convergence of the iterates for the Block Averaging Transformation

Details Gibbsian properties and convergence of the iterates for the Block Averaging Transformation Gibbsian properties and convergence of the iterates for the Block Averaging Transformation

2011-10-27

arxiv.org/abs/1110.6032v1

Markov Processes Relat. Fields 10, 381-394, 2004

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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

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