摘要翻译:
将Sherrington-Kirkpatrick模型自由能的Parisi公式归结为闭式生成泛函。首先给出了Parisi微分方程解的积分表示,并将自由能表示为序参量的泛函。然后在区间$[0,1]$上建立了决定序参量函数的自由能局部极大值的平稳性方程。最后,我们证明了在不诉诸复制技巧的情况下,定态方程的解导致了一个边际稳定的热力学状态。
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英文标题:
《The Parisi formula completed》
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作者:
V. Janis
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最新提交年份:
2007
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分类信息:
一级分类:Physics 物理学
二级分类:Disordered Systems and Neural Networks 无序系统与神经网络
分类描述:Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜;随机、非周期和准周期系统的性质;无序介质中的传输;本地化;由缺陷和无序介导的现象;神经网络
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一级分类:Physics 物理学
二级分类:Statistical Mechanics 统计力学
分类描述:Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变,热力学,场论,非平衡现象,重整化群和标度,可积模型,湍流
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英文摘要:
The Parisi formula for the free energy of the Sherrington-Kirkpatrick model is completed to a closed-form generating functional. We first find an integral representation for a solution of the Parisi differential equation and represent the free energy as a functional of order parameters. Then we set stationarity equations for local maxima of the free energy determining the order-parameter function on interval $[0,1]$. Finally we show without resorting to the replica trick that the solution of the stationarity equations leads to a marginally stable thermodynamic state.
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PDF链接:
https://arxiv.org/pdf/711.1648