Abstract
A set of new critical exponent inequalities,d(1 −1 /δ)≥2 −η, dv(1 − 1/δ)≥γ, anddμ> 1, is proved for a general class of random cluster models, which includes (independent or dependent) percolations, lattice animals (with any interactions), and various stochastic cluster growth models. The inequalities imply that the critical phenomena in the models are inevitably not mean-field-like in the dimensions one, two, and three.
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The present work was reported at the 56th Statistical Mechanics Meeting (Rutgers, December 1986).
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Tasaki, H. Geometric critical exponent inequalities for general random cluster models. J Stat Phys 49, 841–847 (1987). https://doi.org/10.1007/BF01009360
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DOI: https://doi.org/10.1007/BF01009360