Aging in the long-range Ising model

Abstract

The current understanding of aging phenomena is mainly confined to the study of systems with short-ranged interactions. Little is known about the aging of long-ranged systems. Here, the aging in the phase-ordering kinetics of the two-dimensional Ising model with power-law long-range interactions is studied via Monte Carlo simulations. The dynamical scaling of the two-time spin-spin autocorrelator is well described by simple aging for all interaction ranges studied. The autocorrelation exponents are consistent with $\lambda =1.25$ in the effectively short-range regime, while for stronger long-range interactions the data are consistent with $\lambda =d/2=1$. For very long-ranged interactions, strong finite-size effects are observed. We discuss whether such finite-size effects could be misinterpreted phenomenologically as sub-aging.

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• Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
• Dynamical relaxation behaviors of a critical quench
• Quantum aging and dynamical universality in the long-range $O(N\to \infty )$ model
• Ordering Dynamics of the Random Field Long-range Ising Model in One Dimension
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• Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions
• Challenges in identifying simple pattern-forming mechanisms in the development of settlements using demographic data
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