Bethe lattice solution of a model of SAW's with up to 3 monomers per site and no restriction

Abstract

In the multiple monomers per site (MMS) model, polymeric chains are represented by walks on a lattice which may visit each site up to K times. We have solved the unrestricted version of this model, where immediate reversals of the walks are allowed (RA) for K = 3 on a Bethe lattice with arbitrary coordination number in the grand-canonical formalism. We found transitions between a non-polymerized and two polymerized phases, which may be continuous or discontinuous. In the canonical situation, the transitions between the extended and the collapsed polymeric phases are always continuous. The transition line is partly composed by tricritical points and partially by critical endpoints, both lines meeting at a multicritical point. In the subspace of the parameter space where the model is related to SASAW's (self-attracting self-avoiding walks), the collapse transition is tricritical. We discuss the relation of our results with simulations and previous Bethe and Husimi lattice calculations for the MMS model found in the literature.

25 pages, 9 figures

References in corpus (4)

• On a Type of Self-Avoiding Random Walk with Multiple Site Weightings and Restrictions
• Grand canonical and canonical solution of self-avoiding walks with up to three monomers per site on the Bethe lattice
• Solution of a model of self-avoiding walks with multiple monomers per site on the Bethe lattice
• Solution of a model of SAW's with multiple monomers per site on the Husimi lattice

Cited by in corpus (4)

• Nature of the collapse transition in interacting self-avoiding trails
• Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice
• Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge
• Semianalytical solutions of Ising-like and Potts-like magnetic polymers on the Bethe lattice