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This work is dedicated to the study of the discrete version of theMaier-Saupe model in the presence of competing interactions. The competitionbetween interactions favoring different orientational ordering produces a richphase diagram including modulated phases. Using a mean-field approach and MonteCarlo simulations, we show that the proposed model exhibits isotropic andnematic phases and also a series of modulated phases that meet at amulticritical point, a Lifshitz point. Though the Monte Carlo and mean-fieldphase diagrams show some quantitative disagreements, the Monte Carlosimulations corroborate the general behavior found within the mean-fieldapproximation.

Modulated phases in a three-dimensional Maier-Saupe model with competing interactions