Functional renormalization group for multilinear disordered Langevin dynamics II:Revisiting the p = 2 spin dynamics for Wigner and Wishart ensembles

IF 1.1 Q3 PHYSICS, MULTIDISCIPLINARY
Vincent Lahoche, D. Ousmane Samary, M. Tamaazousti
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引用次数: 4

Abstract

In this paper, we investigate the large-time behavior for a slightly modified version of the standard p = 2 soft spins dynamics model, including a quartic or higher potential. The equilibrium states of such a model correspond to an effective field theory, which has been recently considered as a novel paradigm for signal detection in data science based on the renormalization group argument. We consider a Langevin-like equation, including a disorder term that leaves in the Wigner or Wishart ensemble. Then we construct a nonperturbative renormalization group formalism valid in the large N limit, where eigenvalues distributions for the disorder can be replaced by their analytic limits, namely the Wigner and Marchenko-Pastur laws. One of the main advantages of this approach is that the interactions remain local in time, avoiding the non-locality arising from the approaches that integrate out the disorder at the partition function level.
多线性无序Langevin动力学的函数重整化群Ⅱ:Wigner和Wishart系综的p=2自旋动力学
在本文中,我们研究了标准p=2软自旋动力学模型的稍微修改版本的大时间行为,包括四次或更高的电势。这种模型的平衡态对应于有效场论,该理论最近被认为是数据科学中基于重整化群论点的信号检测的新范式。我们考虑一个类朗之万方程,包括一个留在Wigner或Wishart系综中的无序项。然后,我们构造了一个在大N极限下有效的非扰动重整化群形式,其中无序的本征值分布可以用它们的分析极限来代替,即Wigner和Marchenko-Pastur定律。这种方法的主要优点之一是,相互作用在时间上保持局部性,避免了在配分函数水平上整合无序的方法所产生的非局部性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Physics Communications
Journal of Physics Communications PHYSICS, MULTIDISCIPLINARY-
CiteScore
2.60
自引率
0.00%
发文量
114
审稿时长
10 weeks
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