From random to self-avoiding walks |
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Authors: | Cyril Domb |
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Institution: | 1. Physics Department, Bar-Ilan University, Ramat-Gan, Israel
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Abstract: | A brief review will be given of the current situation in the theory of self-avoiding walks (SAWs). The Domb-Joyce model first introduced in 1972 consists of a random walk on a lattice in which eachN step configuration has a weighting factor Π i=0 N?2 Πj=i+2/N(1?ωδij). Herei andj are the lattice sites occupied by the ith and jth points of the walk. When ω=0 the model reduces to a standard random walk, and when ω=1 it is a self-avoiding walk. The universality hypothesis of critical phenomena will be used to conjecture the behavior of the model as a function ofω for largeN. The implications for the theory of dilute polymer solutions will be indicated. |
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