Chaos in Glassy Systems from a TAP Perspective
Chaos in Glassy Systems from a TAP Perspective
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从 TAP 角度看玻璃系统中的混沌
DOI：
10.1103/physrevb.73.064416
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
H. Yoshino
中科院分区：
文献类型：
--
作者：
T. Rizzo;H. Yoshino
本文讨论了在具有一步复制对称破缺（1RSB）的平均场自旋玻璃模型中，随着磁场或温度等外部参数的变化，TAP解的自由能的能级交叉.我们研究的问题，通过广义的复杂性，描述的密度TAP解决方案在给定值的自由能和给定值的广泛的数量共轭的外部参数。我们表明，任何有限数量的外部参数的变化可以诱导自由能广泛不同的TAP状态组之间的能级交叉。在具有1RSB的模型中，这意味着关于扰动的强混沌。由广泛的能级交叉引起的线性响应是自平均的，其值与从低位几乎简并的TAP状态之间的热涨落的二阶矩计算的非自平均异常的无序平均值精确匹配。我们提出了一个计算广义复杂度的解析方法，并在温度变化下的球形多p自旋模型上进行了测试。
We discuss level crossing of the free-energy of TAP solutions under variations of external parameters such as magnetic field or temperature in mean-field spin-glass models that exhibit one-step Replica-Symmetry-Breaking (1RSB). We study the problem through a generalized complexity that describes the density of TAP solutions at a given value of the free-energy and a given value of the extensive quantity conjugate to the external parameter. We show that variations of the external parameter by any finite amount can induce level crossing between groups of TAP states whose free-energies are extensively different. In models with 1RSB, this means strong chaos with respect to the perturbation. The linear-response induced by extensive level crossing is self-averaging and its value matches precisely with the disorder-average of the non self-averaging anomaly computed from the 2nd moment of thermal fluctuations between low-lying, almost degenerate TAP states. We present an analytical recipe to compute the generalized complexity and test the scenario on the spherical multi- p spin models under variation of temperature.