Solution of a model of self-avoiding walks with multiple monomers per site on the Bethe lattice

Abstract

We solve a model of self-avoiding walks with up to two monomers per site on the Bethe lattice. This model, inspired on the Domb-Joyce model, was recently proposed to describe the collapse transition observed in interacting polymers [J. Krawczyk et al, Phys. Rev. Lett. 96, 240603 (2006)]. When immediate self-reversals are allowed (RA model), the solution displays a phase diagram with a polymerized phase and a non-polymerized phase, separated by a phase transition which is of first order for a non-vanishing statistical weight of doubly occupied sites. If the configurations are restricted forbidding immediate self-reversals (RF model), a richer phase diagram is found, displaying a tricritical point and a critical endpoint.

8 pages, 5 figures. Typos corrected, discussion extended, one reference added, style of graphs changed. Version accepted for publication in Phys. Rev. E

References in corpus (2)

• On a Type of Self-Avoiding Random Walk with Multiple Site Weightings and Restrictions
• Series expansion for a stochastic sandpile

Cited by in corpus (9)

• 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 SAW's with multiple monomers per site on the Husimi lattice
• Nature of the collapse transition in interacting self-avoiding trails
• Monte Carlo simulations of polymers with nearest- and next nearest-neighbor interactions on square and cubic lattices
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• Bethe approximation for a DNA-like self-avoiding walk model with variable solvent quality
• Bethe lattice solution of a model of SAW's with up to 3 monomers per site and no restriction
• Collapse transition in polymer models with multiple monomers per site and multiple bonds per edge
• Self-avoiding walks on a bilayer Bethe lattice