Connective constant of the self-avoiding walk on the triangular lattice

The author uses a recently developed Monte Carlo method to study the connective constant of the self-avoiding walk (SAW) on the triangular lattice. Assuming gamma =43/32 one finds mu T =4.15096+or-0.00010+or-0.00026 (95% confidence limits) and mu T =4.15096+or-0.00020+or-0.00037 (99% confidence limits), where the first error bar represents systematic error due to corrections to scaling and the second error bar represents statistical error. This rules out the conjecture mu T + mu H =6 at the greater than 99% confidence level.