Statics and dynamics of the Lebwohl-Lasher model in the Bethe approximation

TL;DR

This paper analyzes the Lebwohl-Lasher model on random graphs, deriving exact phase transition conditions and studying its dynamics through replica theory, with results validated by simulations.

Contribution

It provides the first exact bifurcation conditions for the phase diagram of the Lebwohl-Lasher model on random graphs and explores its dynamics using a novel replica approach.

Findings

Derived exact bifurcation conditions for phase transitions.

Analyzed the model's dynamics with a variant of dynamical replica theory.

Validated theoretical results with simulations.

Abstract

We study the Lebwohl-Lasher model for systems in which spin are arranged on random graph lattices. At equilibrium our analysis follows the theory of spin-systems on random graphs which allows us to derive exact bifurcation conditions for the phase diagram. We also study the dynamics of this model using a variant of the dynamical replica theory. Our results are tested against simulations.