Inter-event time power laws in heterogeneous systems

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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.