Nature of the collapse transition in interacting self-avoiding trails

Abstract

We study the interacting self-avoiding trail (ISAT) model on a Bethe lattice of general coordination $q$ and on a Husimi lattice built with squares and coordination $q=4$. The exact grand-canonical solutions of the model are obtained, considering that up to $K$ monomers can be placed on a site and associating a weight ${\omega }_i$ for a $i$-fold visited site. Very rich phase diagrams are found with non-polymerized (NP), regular polymerized (P) and dense polymerized (DP) phases separated by lines (or surfaces) of continuous and discontinuous transitions. For Bethe lattice with $q=4$ and $K=2$, the collapse transition is identified with a bicritical point and the collapsed phase is associated to the dense polymerized phase (solid-like) instead of the regular polymerized phase (liquid-like). A similar result is found for the Husimi lattice, which may explain the difference between the collapse transition for ISAT's and for interacting self-avoiding walks on the square lattice. For $q=6$ and $K=3$ (studied on the Bethe lattice only), a more complex phase diagram is found, with two critical planes and two coexistence surfaces, separated by two tricritical and two critical end-point lines meeting at a multicritical point. The mapping of the phase diagrams in the canonical ensemble is discussed and compared with simulational results for regular lattices.

12 pages, 13 figures

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Cited by in corpus (7)

• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• Grand-canonical solution of semi-flexible self-avoiding trails on the Bethe lattice
• Polymers with nearest- and next nearest-neighbor interactions on the Husimi lattice
• Polymer models with competing collapse interactions on Husimi and Bethe lattices
• Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares
• 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