Inter-Event Time Power Laws in Heterogeneous Systems

TL;DR

This study reveals that in disordered magnetic systems, the distribution of times between spin flips shifts from exponential in pure systems to power-law in defective ones, highlighting complex relaxation behaviors akin to glassy dynamics.

Contribution

It demonstrates how static disorder causes a transition from exponential to power-law inter-event time distributions in spin systems, revealing new insights into disordered magnetic dynamics.

Findings

Pure systems exhibit exponential IET distributions.

Disordered systems show power-law IET distributions at high temperatures.

At low temperatures, all systems display a universal power-law IET distribution.

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.