# Novel Universality Classes in Ferroelectric Liquid Crystals

## TL;DR

This paper investigates a novel dynamical phase transition in ferroelectric liquid crystals, revealing a new universality class involving a subdiffusive phase and its transition to KPZ behavior under external forcing.

## Contribution

It introduces a new universality paradigm in ferroelectric liquid crystals by combining theoretical analysis and simulations of phase transitions involving SD and KPZ phases.

## Key findings

- Identification of a subdiffusive phase with dynamical exponent 1
- Prediction of a KPZ universality class at equilibrium
- Demonstration of phase flow from SD to KPZ with increased forcing

## Abstract

Starting from a Langevin formulation of a thermally perturbed nonlinear elastic model of the ferroelectric smectic-C$^*$ (SmC${*}$) liquid crystals in the presence of an electric field, this article characterizes the hitherto unexplored dynamical phase transition from a thermo-electrically forced ferroelectric SmC${}^{*}$ phase to a chiral nematic liquid crystalline phase and vice versa. The theoretical analysis is based on a combination of dynamic renormalization (DRG) and numerical simulation of the emergent model. While the DRG architecture predicts a generic transition to the Kardar-Parisi-Zhang (KPZ) universality class at dynamic equilibrium, in agreement with recent experiments, the numerical simulations of the model show simultaneous existence of two phases, one a "subdiffusive" (SD) phase characterized by a dynamical exponent value of 1, and the other a KPZ phase, characterized by a dynamical exponent value of 1.5. The SD phase flows over to the KPZ phase with increased external forcing, offering a new universality paradigm, hitherto unexplored in the context of ferroelectric liquid crystals.