Abstract
The results recently obtained by van Enter, Fernandez, and Sokal on non-Gibbsianness of the measurev =T b μβ,h arising from the application of a single decimation transformationT b , with spacingb, to the Gibbs measure μβ,h , of the Ising model, for suitably chosen large inverse temperatureβ and nonzero external fieldh, are critically analyzed. In particular, we show that if, keeping fixed the same values ofβ, h, andb, one iterates a sufficiently large number of timesn the transformationT b , one obtains a new measurev ′ = (T b )nμβ,h which is Gibbsian and moreover very weakly coupled.
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Martinelli, F., Olivieri, E. Some remarks on pathologies of renormalization-group transformations for the Ising model. J Stat Phys 72, 1169–1177 (1993). https://doi.org/10.1007/BF01048184
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DOI: https://doi.org/10.1007/BF01048184