Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

TL;DR

This study uses Monte Carlo simulations and analytical methods to explore the phase behavior of self-assembled rigid rods on 2D lattices, revealing a continuous isotropic-nematic transition contrary to some theoretical predictions.

Contribution

It provides a comprehensive phase diagram and compares simulation results with mean field and renormalization group theories, clarifying the nature of the transition.

Findings

Monte Carlo simulations show a continuous isotropic-nematic transition.

Mean field theory predicts a first-order transition and tricritical point.

Renormalization group analysis supports a continuous transition.

Abstract

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.