Emergence of Chimeras States in One-dimensional Ising model with Long-Range Diffusion

TL;DR

This paper demonstrates the emergence of chimera-like states in a one-dimensional Ising model with non-local spin diffusion, revealing complex synchronization patterns and phase behaviors relevant to neural media.

Contribution

It introduces a novel non-local diffusion setup in the Ising model to study chimera states, combining analytical and simulation methods to explore their conditions and behaviors.

Findings

First observation of chimera-like states in Ising systems

Identification of phase diagram with diverse dynamical regimes

Analysis of metastable chimeras decaying into stable domains

Abstract

In this work, we examine the conditions for the emergence of chimera-like states in Ising systems. We study an Ising chain with periodic boundaries in contact with a thermal bath at temperature T, that induces stochastic changes in spin variables. To capture the non-locality needed for chimera formation, we introduce a model setup with non-local diffusion of spin values through the whole system. More precisely, diffusion is modeled through spin-exchange interactions between units up to a distance R, using Kawasaki dynamics. This setup mimics, e.g., neural media, as the brain, in the presence of electrical (diffusive) interactions. We explored the influence of such non-local dynamics on the emergence of complex spatiotemporal synchronization patterns of activity. Depending on system parameters we report here for the first time chimera-like states in the Ising model, characterized by relatively stable moving domains of spins with different local magnetization. We analyzed the system at T=0, both analytically and via simulations and computed the system's phase diagram, revealing rich behavior: regions with only chimeras, coexistence of chimeras and stable domains, and metastable chimeras that decay into uniform stable domains. This study offers fundamental insights into how coherent and incoherent synchronization patterns can arise in complex networked systems as it is, e.g., the brain.