Abstract
We use the algorithm recently introduce by A. Berretti and A. D. Sokal to compute numerically the critical exponents for the self-avoiding random walk on the hexagonal lattice. We findγ=1.3509±0.0057±0.0023v=0.7580±0.0049±0.0046α=0.519±0.082±0.077 where the first error is the systematic one due to corrections to scaling and the second is the statistical error. For the effective coordination numberμ we findμ=1.84779±0.00006±0.0017 The results support the Nienhuis conjectureγ=43/32 and provide a rough numerical check of the hyperscaling relationdv=2−α. An additional analysis, taking the Nienhuis value ofμ=(2+21/2)1/2 for granted, givesγ=1.3459±0.0040±0.0008
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de Forcrand, P., Koukiou, F. & Petritis, D. Self-avoiding random walks on the hexagonal lattice. J Stat Phys 45, 459–470 (1986). https://doi.org/10.1007/BF01021082
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DOI: https://doi.org/10.1007/BF01021082