Inter-Event Time Power Laws in Heterogeneous Systems

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.

11 pages, 5 figures

References in corpus (15)

• Power-law distributions in empirical data
• The origin of bursts and heavy tails in human dynamics
• Modeling bursts and heavy tails in human dynamics
• Human Dynamics: The Correspondence Patterns of Darwin and Einstein
• An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
• Kinetic Ising model in an oscillating field: Finite-size scaling at the dynamic phase transition
• Universality in the three-dimensional random-field Ising model
• Fragmentation of shells
• Scaling of impact fragmentation near the critical point
• Strain intermittency in shape-memory alloys
• New Power Law Signature of Media Exposure in Human Response Waiting Time Distributions
• The Effect of Defects on Magnetic Droplet Nucleation
• Finite-temperature avalanches in 2D disordered Ising models
• Dynamic Phase Transition in 2D Ising Systems: Effect of Anisotropy and Defects
• Scaling of Static and Dynamical Properties of Random Anisotropy Magnets