Spin Diffusion Constant Changes Sharply under Integrability Breaking of Classical Magnets

The fundamental process of diffusion, whereby particles spread out from areas of high concentration, underpins many physical phenomena, yet understanding its microscopic origins in complex, interacting systems remains a significant challenge. Jiaozi Wang, from the University of Osnabrück, Sourav Nandy of the Max Planck Institute for the Physics of Complex Systems, Markus Kraft from the University of Osnabrück, and colleagues now investigate how diffusion behaves when a perfectly ‘integrable’ system, one where energy is conserved in predictable ways, experiences subtle disruptions. Their research focuses on a model magnetic material and reveals a dramatic change in the rate of spin diffusion as the system moves away from perfect integrability, alongside a shift in the statistical behaviour of how magnetism spreads. These findings suggest that even systems designed to resist change exhibit surprisingly complex diffusion mechanisms when perturbed, offering new insights into the behaviour of interacting particles and the breakdown of predictable behaviour in physical systems.

Diffusion Emerges From Weakly Broken Integrability

Researchers investigate how diffusion arises in classical magnetic systems when their perfect order is slightly disturbed, moving beyond simplified scenarios. The approach involves analysing the dynamics of initially localised disturbances within these magnetic systems, tracking their spread and characterising the resulting transport behaviour. Specifically, the team examines the emergence of diffusive behaviour and determines how the diffusion constant scales with the strength of the disturbance. The results demonstrate that even weak disturbances can induce diffusive behaviour, and the team identifies a universal scaling relation between the diffusion constant and the disturbance strength, holding across a range of magnetic systems and disturbance types. This scaling relation reveals a logarithmic dependence of the diffusion constant on the disturbance strength, indicating a slow but persistent increase in transport with increasing levels of disorder. The findings provide insights into the fundamental mechanisms governing transport in many-body systems, with implications for condensed matter physics and quantum information theory.

Diffusion Transition Reveals Non-Analytic Behaviour

This research has revealed key insights into the microscopic origins of diffusion in interacting physical systems, specifically within a classical spin model subjected to small disturbances. Through large-scale numerical simulations, scientists demonstrated a distinct change in the spin diffusion constant as the strength of these disturbances increases, indicating a fundamental shift in the diffusion mechanism itself. This change occurs at a specific point, suggesting a non-analytic dependence of the diffusion constant on the disturbance strength, a phenomenon also observed in quantum systems. Furthermore, the team investigated the statistical nature of magnetization transfer, finding a transition from non-Gaussian to Gaussian behaviour as integrability is broken.

This change, reflected in the behaviour of higher-order statistical measures, suggests a restoration of normal diffusive transport under these conditions. The researchers established a clear scaling relationship between the diffusion constant, system size, and disturbance strength, providing a quantitative understanding of this behaviour. These findings contribute to a growing understanding of transport phenomena in near-integrable systems and offer a classical analogue to recent observations in quantum spin chains, potentially strengthening the connection between classical and quantum physics in this area.

Diffusion, Lyapunov Exponents, and Scaling Analysis

This supplementary material provides strong supporting evidence and analysis for the claims made in the main text. It comprehensively covers multiple lines of evidence, including the time-dependent diffusion constant, higher-order cumulants, and maximum Lyapunov exponents. The data demonstrates a crossover from integrable to chaotic behaviour, with the maximum Lyapunov exponent converging with increasing system size and scaling as √ε, indicating a transition from integrability to chaos. The rescaled cumulant κn(t) deviates from integrable behaviour at a time scale t* that scales as ε^-2. The supplementary material directly supports and expands upon the arguments made in the main paper, addressing potential concerns by showing data for different system sizes. The inclusion of quantitative results, such as the scaling of Lyapunov exponents, adds rigor to the analysis. The authors have gone above and beyond to provide detailed evidence and analysis to support their claims.