# Domain percolation in a quenched ferromagnetic spinor condensate

## TL;DR

This paper demonstrates that magnetic domain formation in a quenched ferromagnetic spinor condensate can be described by percolation theory, providing insights into phase transition behavior through simulations and finite-size scaling analysis.

## Contribution

It introduces a generalized spin rotation method to control domain proportions and explores percolation properties in the system, linking magnetic domain dynamics to percolation theory.

## Key findings

- Finite-size scaling reveals the correlation length critical exponent.
- Identification of the percolation transition point.
- Sensitivity analysis of early-time dynamics and external parameters.

## Abstract

We show that the easy-axis (EA) magnetic domains formed in a quenched ferromagnetic spinor condensate are described by percolation theory. We introduce a generalized spin rotation to vary the proportion of positive and negative EA domains, allowing us to explore domain percolation. Using simulations we investigate the finite-size scaling behaviour to extract the correlation length critical exponent and the transition point. We analyse the sensitivity of our results to the early-time dynamics of the system, the quadratic Zeeman energy, and the threshold condition used to define the positive (percolating) domains.