# Complex free energy landscapes in biaxial nematics and role of repulsive interactions : A Wang - Landau study

## TL;DR

This study uses Wang-Landau sampling to explore complex free energy landscapes in biaxial nematics, highlighting the significant impact of cross-coupling interactions on phase stability and organization.

## Contribution

It reveals the destabilizing influence of cross-coupling interactions on biaxial phases, challenging mean field and standard Monte Carlo predictions.

## Key findings

- Increased cross-coupling leads to local biaxial organizations.
- Complex free energy landscapes hinder laboratory realization of biaxial phases.
- Biaxial order appears inhomogeneously within uniaxial phases.

## Abstract

General quadratic Hamiltonian models, describing interaction between crystal molecules (typically with $D_{2h}$ symmetry) take into account couplings between their uniaxial and biaxial tensors. While the attractive contributions arising from interactions between similar tensors of the participating molecules provide for eventual condensation of the respective orders at suitably low temperatures, the role of cross-coupling between unlike tensors is not fully appreciated. Our recent study with an advanced Monte Carlo technique (entropic sampling) showed clearly the increasing relevance of this cross term in determining the phase diagram, contravening in some regions of model parameter space, the predictions of mean field theory and standard Monte Carlo simulation results. In this context, we investigated the phase diagrams and the nature of the phases therein, on two trajectories in the parameter space: one is a line in the interior region of biaxial stability believed to be representative of the real systems, and the second is the extensively investigated parabolic path resulting from the London dispersion approximation. In both the cases, we find the destabilizing effect of increased cross-coupling interactions, which invariably result in the formation of local biaxial organizations inhomogeneously distributed. This manifests as a small, but unmistakable, contribution of biaxial order in the uniaxial phase.The free energy profiles computed in the present study as a function of the two dominant order parameters indicate complex landscapes, reflecting the difficulties in the ready realization of the biaxial phase in the laboratory.