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

## TL;DR

This paper investigates a three-dimensional Maier-Saupe model with competing interactions, revealing a complex phase diagram with isotropic, nematic, and modulated phases, and identifying a Lifshitz point through mean-field and Monte Carlo methods.

## Contribution

It introduces a discrete Maier-Saupe model with competing interactions and demonstrates the existence of modulated phases and a Lifshitz point using combined mean-field and Monte Carlo approaches.

## Key findings

- Identification of isotropic, nematic, and modulated phases.
- Existence of a Lifshitz point where phases meet.
- Qualitative agreement between Monte Carlo and mean-field results.

## Abstract

This work is dedicated to the study of the discrete version of the Maier-Saupe model in the presence of competing interactions. The competition between interactions favoring different orientational ordering produces a rich phase diagram including modulated phases. Using a mean-field approach and Monte Carlo simulations, we show that the proposed model exhibits isotropic and nematic phases and also a series of modulated phases that meet at a multicritical point, a Lifshitz point. Though the Monte Carlo and mean-field phase diagrams show some quantitative disagreements, the Monte Carlo simulations corroborate the general behavior found within the mean-field approximation.