- 99-197 Bertini L., Cirillo E.N.M., Olivieri E.
- Renormalization Group Transformations under strong mixing conditions:
gibbsianess and convergence of renormalized interactions
(124K, TeX Plain)
May 28, 99
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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.
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