Solution of semi-flexible self-avoiding trails on a Husimi lattice built with squares

Abstract

We study a model of semi-flexible self-avoiding trails, where the lattice paths are constrained to visit each lattice edge at most once, with configurations weighted by the number of collisions, crossings and bends, on a Husimi lattice built with squares. We find a rich phase diagram with five phases: a non-polymerised phase ($\mathbf{NP}$), low density ($P1$) and high density ($P2$) polymerised phases, and, for sufficiently large stiffness, two additional anisotropic (nematic) ($AN1$ and $AN2$) polymerised phases within the $P1$ phase. Moreover, the {\bf AN1} phase which shows a broken symmetry with a preferential direction, is separated from the $P1$ phase by the other nematic $AN2$ phase. Although this scenario is similar to what was found in our previous calculation on the Bethe lattice, where the $\mathbf{AN}-P1$ transition was discontinuous and critical, the presence of the additional nematic phase between them introduces a qualitative difference. Other details of the phase diagram are that a line of tri-critical points may separate the $P1-P2$ transition surface into a continuous and a discontinuous portion, and that the same may happen at the $\mathbf{NP}-P1$ transition surface, details of which depend on whether crossings are allowed or forbidden. A critical end-point line is also found in the phase diagram.

arXiv comment21 pages, 10 figures

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Cited by in corpus (3)

• Husimi lattice solutions and the coherent-anomaly-method analysis for hard-square lattice gases
• Semi-flexible compact polymers in two dimensional nonhomogeneous confinement
• Semianalytical solutions of Ising-like and Potts-like magnetic polymers on the Bethe lattice