Inter-event time power laws in heterogeneous systems

¹ Department of Physics, Politecnico di Milano - Piazza Leonardo da Vinci 32, 20133 Milan, Italy
² School of Mathematical Sciences, University of Southampton - University Road, Highfield, Southampton, SO17 1BJ, UK

Received: 15 November 2024
Accepted: 15 January 2025

Abstract

We investigate the dynamic behavior of spin reversal events in the dilute Ising model, focusing on the influence of static disorder introduced by pinned spins. Our Monte Carlo simulations reveal that in a homogeneous, defect-free system, the inter-event time (IET) between local spin flips follows an exponential distribution, characteristic of Poissonian processes. However, in heterogeneous systems where defects are present, we observe a significant departure from this behavior. At high temperatures, the IET exhibits a power-law distribution resulting from the interplay of spins located in varying potential environments, where defect density influences reversal probabilities. At low temperatures, all site classes converge to a unique power-law distribution, regardless of their potential, leading to distinct critical exponents for the high- and low-temperature regimes. This transition from exponential to power-law behavior underscores the critical response features of magnetic systems with defects, suggesting analogies to glassy dynamics. Our findings highlight the complex mechanisms governing spin dynamics in disordered systems, with implications for understanding the universal aspects of relaxation in glassy materials.