Sequence of phase transitions in a model of interacting rods

TL;DR

This paper investigates multiple phase transitions in a 2D lattice model of interacting rods, revealing both Ising-type and geometrical transitions with complex phase diagrams through simulations and analytical methods.

Contribution

It introduces a comprehensive analysis of phase transitions in a lattice model of rods, highlighting the coexistence of symmetry-breaking and geometrical transitions with varying parameters.

Findings

Multiple phase transitions identified, including Ising-type and geometrical.

Phase boundaries can cross, creating complex phase behavior.

Results obtained via Monte Carlo simulations and fixed-point analysis.

Abstract

In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa=\ell/a$ and the temperature are varied. There are essentially two classes of transitions. One corresponds to the Ising-type spontaneous symmetry breaking transition and the second belongs to less-studied phase transitions of geometrical origin. The latter class of transitions appear at fixed values of $\kappa$ irrespective of the temperature, whereas the critical coupling for the spontaneous symmetry breaking transition depends on it. By varying the temperature, the phase boundaries may cross each other, leading to a rich phase behaviour with infinitely many phases. Our results are based on Monte Carlo simulations on the square lattice, and a fixed-point analysis of a functional flow equation on a Bethe lattice.