Polymer chain statistics and universality. I
- 1 February 1978
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 11 (2), 361-374
- https://doi.org/10.1088/0305-4470/11/2/013
Abstract
A brief summary is given of the concept of universality in the theory of critical phenomena. The concept is applied to random walks and self-avoiding walks on lattices corresponding to the n=-2 and n=0 universality classes. The Domb-Joyce model of a random walk on a lattice with a delta function interaction of strength w is identified with crossover behaviour, w serving as a crossover parameter. Exact enumerations are undertaken of the mean-square end-to-end length (RN2) for the Domb-Joyce model for a number of three-dimensional lattices. Using the smoothness postulate of Griffiths, estimates are obtained of the asymptotic behaviour of the expansion factor alpha 2=(RN2)/N in the range 0.52 is a function of wN1/2 is satisfied with maximum errors of 2 or 3%. The two-parameter function which has been the subject of much discussion by polymer theorists is estimated and an empirical formula is proposed.Keywords
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