Swarmalators with thermal noise
Hyunsuk Hong, Kevin O’Keeffe, Jae Sung Lee, Hyunggyu Park
Abstract
We investigate a population of swarmalators, mobile versions of phase oscillators that both sync in time and swarm through space. We focus on an $XY$-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.