New spin model for the biased self-avoiding walk

David Atkatz, Gerrit Ten Brinke, J. W. Halley, H. Nakanishi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We present a new spin model for the biased self-avoiding walk on the square lattice. Unlike a previous model containing both vector and Ising spins, our model contains only n-vector spins, evaluated in the n0 limit, and the spin Hamiltonian is Hermitian. Integration over one of the three sets of spins leads to a rigorous proof that the crossover exponent from straight chain to random walk behavior is 1. An analysis of the scaling behavior of the Hamiltonian in the small gauche-bond probability limit enables us to conclude that self-interaction effects in the biased walk will be irrelevant in three dimensions, but not in two dimensions, in agreement with some earlier numerical results.

Original languageEnglish (US)
Pages (from-to)5500-5506
Number of pages7
JournalPhysical Review B
Issue number10
StatePublished - 1987

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