The lattice version of the Maier-Saupe model of a nematic liquid crystal, in which all molecules are restricted to be on a simple-cubic lattice with periodic boundary conditions and to interact only with their nearest neighbors through the interaction energy $E_{\mathrm{ij}}=-\epsilon (\frac{3}{2}{{cos}^2\theta }_{\mathrm{ij}}-\frac{1}{2})$, is investigated using a Monte Carlo technique. The lattice is found to undergo a first-order phase transition at $\frac{\epsilon }{\mathrm{kT}}=0.890\mathrm{}\pm 0.005$ with a spontaneous order of $〈P_2\left(cos\theta \right)〉=0.33\mathrm{}\pm 0.04$ at the transition.

• Received 1 March 1972

DOI:https://doi.org/10.1103/PhysRevA.6.426