临界交叉概率的均匀有界性意味着超尺度

Random Struct. Algorithms Pub Date : 1999-10-01 DOI:10.1002/(SICI)1098-2418(199910/12)15:3/4%3C368::AID-RSA9%3E3.0.CO;2-B

C. Borgs, J. Chayes, H. Kesten, J. Spencer

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Uniform boundedness of critical crossing probabilities implies hyperscaling

We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 15, 368–413, 1999

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Random Struct. Algorithms

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