Anomalous Ising freezing times

Denholm, J and Hourahine, B (2020) Anomalous Ising freezing times. Journal of Statistical Mechanics: Theory and Experiment, 2020. 093205. ISSN 1742-5468 (https://doi.org/10.1088/1742-5468/abb0df)

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Abstract

We measure the relaxation time of a square lattice Ising ferromagnet that is quenched to zero-temperature from supercritical initial conditions. We reveal an anomalous and seemingly overlooked timescale associated with the relaxation to ‘frozen’ two-stripe states. While close to a power law of the form ∼ L^ν , we argue this timescale actually grows as L^2 ln L, with L the linear dimension of the system. We uncover the mechanism behind this scaling form by using a synthetic initial condition that replicates the late time ordering of two-stripe states, and subsequently explain it heuristically.

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