# Modulated structures in a Lebwohl-Lasher model with chiral interactions

## TL;DR

This paper introduces a chiral nematic clock model based on a Lebwohl-Lasher lattice with planar nematic directors, analyzing its phase structures and the effects of temperature and chirality on modulated phases using a non-linear map approach.

## Contribution

It develops a novel chiral $p$-state nematic clock model and explores its complex phase behavior using a discrete non-linear map on a Cayley tree, revealing new chiral nematic phases.

## Key findings

- Multiple chiral nematic phases identified
- Temperature and chirality influence modulation structures
- Uniform and periodic phases depend on model parameters

## Abstract

We consider a Lebwohl-Lasher lattice model with nematic directors restricted to point along $p$ planar directions. This $XY$ Lebwohl-Lasher system is the nematic analogue of the standard $p$-state clock model. We then include chiral interactions, and introduce a chiral $p$-state nematic clock model. The statistical problem is formulated as a discrete non-linear map on a Cayley tree. The attractors of this map correspond to the physical solutions deep in the interior of the tree. It is possible to observe uniform and periodic structures, depending on temperature and a parameter of chirality. We find many different chiral nematic phases, and point out the effects of temperature and chirality on the modulation associated with these structures.