# Patterns of polar domains in a spatiotemporal model of interacting polarities

## TL;DR

This paper introduces a novel physical model for polarity fields that captures long-distance pattern formation through effective transport and interactions, revealing new steady-state configurations and transitions.

## Contribution

It presents an original lattice-based model incorporating transport, external fields, and interactions to explain polarity pattern formation in physical systems.

## Key findings

- Identification of two main steady-state configurations
- Characterization of pattern transitions
- Potential mechanisms for polarity pattern generation

## Abstract

Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical model that generalizes classical spin models on a lattice by incorporating effective transport of polarity molecules between neighboring sites. We account for an external field and for ferromagnetic interactions between sites and prescribe the time-evolution of the system using two distinct dissipative classes for non-conserved and conserved variables representing polarity orientation and magnitude, respectively. We observe two main types of steady-state configurations --disordered configurations and patterns of highly polar spots surrounded by regions with low polarity-- and we characterise patterns and transitions between configurations. Our results may provide alternative pattern-generating mechanisms for materials endowed with polarity fields.