Hard rigid rods on Husimi lattices

TL;DR

This study analyzes the phase transitions of hard rigid rods on Husimi lattices, revealing isotropic-nematic transitions for rods of size four or more, with transition types and critical parameters depending on lattice geometry.

Contribution

It provides the first detailed analysis of rod behavior on Husimi lattices, showing how lattice structure influences phase transition nature and critical parameters.

Findings

Isotropic phase for dimers and trimers; nematic transition for rods of size ≥4.

Continuous transition in square Husimi lattice; discontinuous in triangular.

Critical activities and densities decrease with rod size; entropy closely matches exact results.

Abstract

We study the thermodynamic behavior of hard rigid rods of size $k$ (i.e., $k$-mers) on four- and six-coordinated Husimi lattices (HLs), respectively built with squares (square HL) and triangles (triangular HL). In both lattices, dimers ($k=2$) and trimers ($k=3$) only present a isotropic phase, whereas a isotropic-nematic transition is observed for $k \ge 4$. In the square HL, this transition is continuous and occurs at a critical \textit{monomer} activity which displays a nonmonotonic variation with $k$, while the critical \textit{rod} activity and density are always decreasing functions of $k$. The isotropic-nematic transition is discontinuous in the triangular HL, but the $k$-dependence of the coexistence activities and density is analogous to that found for the square case. No transition from the nematic to a high-density disordered phase is found in these HLs. In general, this scenario is very similar to that already observed for rods on the Bethe lattice, though the critical parameters obtained here are in most cases closer to those reported in the literature for the square and triangular lattices. The entropy per site of fully-packed rods is also investigated in detail in the triangular HL, where its value for dimers differs by only 0.7\% from the exact result for the triangular lattice.