Re-entrant Disordered Phase in a System of Repulsive Rods on a Bethe-like Lattice

TL;DR

This paper provides an exact solution for a model of rigid rods with repulsive interactions on a Bethe-like lattice, revealing complex phase behavior including re-entrant disordered phases and phase transition characteristics depending on system parameters.

Contribution

It introduces an exact analytical solution for the phase diagram of monodispersed rods on a Bethe-like lattice, highlighting re-entrant disordered phases and transition types.

Findings

Re-entrant disordered phase at high density for rods with length ≥ 4.

Continuous phase transitions in the case of coordination number 4.

Discontinuous transition observed for higher even coordination numbers.

Abstract

We solve exactly a model of monodispersed rigid rods of length $k$ with repulsive interactions on the random locally tree like layered lattice. For $k\geq 4$ we show that with increasing density, the system undergoes two phase transitions: first from a low density disordered phase to an intermediate density nematic phase and second from the nematic phase to a high density re-entrant disordered phase. When the coordination number is $4$, both the phase transitions are continuous and in the mean field Ising universality class. For even coordination number larger than $4$, the first transition is discontinuous while the nature of the second transition depends on the rod length $k$ and the interaction parameters.