On the critical behaviour of self-avoiding walks

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Abstract
For the self-avoiding walk problem the series expansions of the chain generating function and mean square end-to-end distance generating function have been extended to 27 steps for the square lattice and to 20 steps for the simple cubic lattice. The author develops an analysis protocol based on the method of integral approximants. Using this protocol the author finds excellent agreement with Nienhuis' exact exponent values (1984) in two dimensions gamma =1.34375 and nu =0.750. In three dimensions the author finds gamma =1.162+or-0.002 and nu =0.592+or-0.002. Accurate estimates of the critical point (reciprocal of the connective constant) for several two- and three dimensional lattices are also obtained.

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