退火无序线性系统的动态平均场理论精确解

Francesco Ferraro, Christian Grilletta, Amos Maritan, Samir Suweis, Sandro Azaele
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引用次数: 0

摘要

我们研究了一个无序的多维线性系统,其中的相互作用参数随时间随机变化,并具有确定的时间相关性。我们将这种无序称为 "退火",与耦合在时间上固定不变的淬火无序形成对比。我们扩展了动态平均场理论,以适应退火无序状态,并利用该理论找到线性模型在大量自由度极限下的精确解。我们的分析得出了模型的非静态自相关、静态方差、功率谱密度和相图的分析结果。有趣的是,在改变相互作用的相关时间后,出现了一些意想不到的特征。我们发现系统的静态方差和无序的临界方差通常是相互作用相关时间的非单调函数。我们还发现,在某些情况下,当相关时间改变时,会发生重入相变。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder
We investigate a disordered multi-dimensional linear system in which the interaction parameters vary stochastically in time with defined temporal correlations. We refer to this type of disorder as "annealed", in contrast to quenched disorder in which couplings are fixed in time. We extend Dynamical Mean-Field Theory to accommodate annealed disorder and employ it to find the exact solution of the linear model in the limit of a large number of degrees of freedom. Our analysis yields analytical results for the non-stationary auto-correlation, the stationary variance, the power spectral density, and the phase diagram of the model. Interestingly, some unexpected features emerge upon changing the correlation time of the interactions. The stationary variance of the system and the critical variance of the disorder are generally found to be a non-monotonic function of the correlation time of the interactions. We also find that in some cases a re-entrant phase transition takes place when this correlation time is varied.
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