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 n\ensuremath{\rightarrow}0 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
