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Anomalous Ising freezing times
Journal of Statistical Mechanics: Theory and Experiment ( IF 2.4 ) Pub Date : 2020-09-23 , DOI: 10.1088/1742-5468/abb0df
J Denholm , B Hourahine

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 $\sim L^{\nu}$ , we argue this timescale actually grows as $\sim L^{2}\ln L$, 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.

中文翻译:

异常伊辛冰冻时间

我们测量了从超临界初始条件淬火到零温度的方形晶格 Ising 铁磁体的弛豫时间。我们揭示了一个与“冻结”两条纹状态的松弛相关的异常且看似被忽视的时间尺度。虽然接近 $\sim L^{\n​​u}$ 形式的幂律,但我们认为这个时间尺度实际上随着 $\sim L^{2}\ln L$ 增长,L 是系统的线性维度。我们通过使用一个合成的初始条件来揭示这种缩放形式背后的机制,该条件复制了双条带状态的后期时间排序,并随后对其进行了启发式解释。
更新日期:2020-09-23
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