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摘要翻译：
在p体Sherrington-Kirkpatrick模型中，用复制数n为有限的复制方法计算了自由能的累积量母函数phi(n)和速率函数Sigma(f)。从扰动论元出发，我们证明了累积量母函数在n=0附近是常数。另一方面，借助phi(n)的两个解析性质，再次导出了phi(n)的行为。然而，这也被证明是在有限的n值时被打破的，这给出了速率函数中的特征值，靠近自由能的热力学值。通过将phi(n)延拓为n的函数，我们找到了至少在该模型中导出1RSB解的一种方法，即将RS解固定为单调递增函数。
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英文标题：
《Large Deviation Property of Free Energy in p-Body
Sherrington-Kirkpatrick Model》
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作者：
Tetsuya Nakajima and Koji Hukushima
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最新提交年份：
2008
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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：
Cumulant generating function phi(n) and rate function Sigma(f) of the free energy is evaluated in p-body Sherrington-Kirkpatrick model by using the replica method with the replica number n finite. From a perturbational argument, we show that the cumulant generating function is constant in the vicinity of n = 0. On the other hand, with the help of two analytic properties of phi(n), the behavior of phi(n) is derived again. However this is also shown to be broken at a finite value of n, which gives a characteristic value in the rate function near the thermodynamic value of the free energy. Through the continuation of phi(n) as a function of n, we find out a way to derive the 1RSB solution at least in this model, which is to fix the RS solution to be a monotone increasing function.
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PDF链接：
https://arxiv.org/pdf/802.1302
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