Application of the method of Pade approximants to the excluded volume problem

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Abstract
Pade approximants have been applied to the analysis of the chain generating functions of all the common two- and three-dimensional lattices. Estimates for the critical attrition mu , are in very close agreement with those obtained using the ratio method. The index, g, is estimated as 0.330+or-0.003 for the triangular lattice and 0.1663+or-0.0003 for the face-centred-cubic. These estimates are consistent with the hypothesis that g=1/3 exactly in two dimensions and g=1/6 exactly in three dimensions. These values have been used to form estimates for the critical amplitudes, A. The Pade approximants provide further evidence for the existence of an 'antiferromagnetic singularity' in the chain generating functions of the loose-packed lattices.

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