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

We study the Lebwohl–Lasher model for systems in which spins 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.