Spin-glass theory for pedestrians
Spin-glass theory for pedestrians
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DOI：
10.1088/1742-5468/2005/05/p05012
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发表时间：
2005-05-01
影响因子：
2.4
通讯作者：
Cavagna, A
中科院分区：
文献类型：
--
作者：
Castellani, T;Cavagna, A
在这些笔记中，以紧凑和教学的方式回顾了平均场自旋玻璃领域的主要理论概念和技术，以供研究生和本科生参考。使用三种不同的方法分析一种特定的自旋玻璃模型（p-自旋球模型）：热力学、覆盖纯态、重叠、重叠分布、复制对称破缺和静态转变；动力学，涵盖生成函数方法、广义朗之万方程、相关方程和响应方程、模态耦合近似和动态转变；最后是复杂性，涵盖平均场（Thouless-Anderson-Palmer）自由能、亚稳态、熵危机、阈值能量和鞍座。特别注意不同方法获得的结果的相互一致性。
In these notes the main theoretical concepts and techniques in the field of mean-field spin glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is analysed (the p-spin spherical model) by using three different approaches: thermodynamics, covering pure states, overlaps, overlap distribution, replica symmetry breaking, and the static transition; dynamics, covering the generating functional method, generalized Langevin equation, equations for the correlation and the response, the mode coupling approximation, and the dynamical transition; and finally complexity, covering the mean-field (Thouless-Anderson-Palmer) free energy, metastable states, entropy crisis, threshold energy, and saddles. Particular attention has been paid to the mutual consistency of the results obtained from the different methods.