# Swarmalators with thermal noise

## TL;DR

This paper studies a one-dimensional model of swarmalators influenced by thermal noise, revealing four collective states and providing a detailed phase diagram that aligns well with simulations, offering insights into thermal self-synchronizing and self-assembling systems.

## Contribution

It introduces a tractable XY-type model of swarmalators with thermal noise, identifying multiple collective states and deriving an accurate phase diagram.

## Key findings

- Identification of four distinct collective states.
- Discovery of a mixed state blending two behaviors.
- High-accuracy phase diagram matching simulations.

## Abstract

We investigate a population of swarmalators, a mobile version of phase oscillators that both sync in time and swarm through space. We focus on a XY-type model of identical swarmalators running on a one-dimensional ring and subject to thermal noise. We uncover four distinct collective states, some of which capture the behavior of real-world swarmalators such as vinegar eels and sperm. Among these, the most intriguing is the `mixed state', which blends two of the other states. We present a comprehensive phase diagram from the Fourier mode analysis with a high accuracy, which is in excellent agreement with numerical simulation results. Our model serves as a tractable toy model for thermal systems that both self-synchronize and self-assemble interdependently.