Cugliandolo-Kurchan equations for dynamics of Spin-Glasses
Cugliandolo-Kurchan equations for dynamics of Spin-Glasses
复制标题
自旋玻璃动力学的 Cugliandolo-Kurchan 方程
DOI：
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发表时间：
2004
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通讯作者：
A. Guionnet
中科院分区：
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作者：
Gérard Ben Arous;A. Dembo;A. Guionnet
研究了统计物理中球形p自旋无序平均场模型族的朗之万动力学。我们证明了在系统大小N趋近于无穷极限时，这些N维耦合扩散的经验状态相关函数和积分响应函数在时间上几乎肯定地一致收敛于由Cugliandolo和Kurchan深入研究的一对显式非线性积分微分方程的非随机唯一强解。
We study the Langevin dynamics for the family of spherical p-spin disordered mean-field models of statistical physics. We prove that in the limit of system size N approaching infinity, the empirical state correlation and integrated response functions for these N-dimensional coupled diffusions converge almost surely and uniformly in time, to the non-random unique strong solution of a pair of explicit non-linear integro-differential equations intensively studied by Cugliandolo and Kurchan.