# A multiscale approach to liquid crystal nematics via statistical field theory

## TL;DR

This paper develops a multiscale statistical field theory approach to relate macroscopic Landau-de Gennes parameters to a microscopic lattice gas model of nematic molecules, providing insights into phase transition conditions.

## Contribution

It introduces a method to connect Landau-de Gennes free energy coefficients with a microscopic molecular model for uniaxial nematics, enhancing understanding of phase stability.

## Key findings

- Derived constraints on temperature and volume fraction for stability.
- Predicted isotropic-nematic transition temperature and order parameter discontinuity.
- Good agreement with Monte Carlo simulation results.

## Abstract

We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients $A$, $B$, $C$, $L_1$ and $L_2$ of the Landau-de Gennes free energy for the isotropic-nematic phase transition to the parameters of a molecular model of uniaxial nematics, which we take to be a lattice gas model of nematogenic molecules interacting via a short-ranged potential. We obtain general constraints on the temperature and volume fraction of nematogens for the Landau-de Gennes theory to be stable against molecular orientation fluctuations at quartic order. In particular, for the case of a fully occupied lattice, we compute the values of the isotropic-nematic transition temperature and the order parameter discontinuity predicted by (i) a continuum approximation of the nearest-neighbor Lebwohl-Lasher model and (ii) a Lebwohl-Lasher-type model with a nematogenic interaction of finite range. We find that the predictions of (i) are in reasonably good agreement with known results of MC simulation.