Abstract
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 language | English (US) |
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Pages (from-to) | 5500-5506 |
Number of pages | 7 |
Journal | Physical Review B |
Volume | 36 |
Issue number | 10 |
DOIs | |
State | Published - 1987 |