Self-avoiding random walks on the hexagonal lattice

The authors use the algorithm recently introduced by A. Berretti and A.D. Sokal to compute numerically the critical exponents for the self-avoiding random walk on the hexagonal lattice. They find γ = 1.3509 +/- 0.0057 +/- 0.0023; v = 0.7580 +/- 0.0049 +/- 0.0046; α = 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 number μ they find μ = 1.84779 +/- 0.00006 +/- 0.0017. The results support the Nienhuis conjecture γ = 43/32 and provide a rough numerical check of the hyperscaling relation dv = 2 - α. An additional analysis, taking the Nienhuis value of μ = (2 + 2/sup 1/2/)/sup 1/2/ for granted, gives γ = 1.3459 +/- 0.0040 +/- 0.0008