Replica Plefka expansion of Ising systems
Replica Plefka expansion of Ising systems
复制标题
Ising 系统的复制品 Plefka 扩展
DOI：
10.1088/1742-5468/2012/04/p04002
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Yoshiyuki Kabashima and Kazuyuki Tanaka
中科院分区：
文献类型：
--
作者：
Muneki Yasuda;Yoshiyuki Kabashima and Kazuyuki Tanaka
为了研究自旋玻璃系统在复制对称性破缺阶段的行为，发展了复制扩展理论。副本扩展理论是针对特定样本的副本理论，具有一步副本对称破缺的方案。本文利用Plefka展开，提出了Ising系统Gibbs自由能的微扰展开式，并给出了二阶和三阶近似的显式表达式。我们的Plefka扩展系统地提供了微扰近似考虑一步复制对称破缺。在一些数值实验中，我们表明，我们的微扰近似是定量的上级传统的微扰近似，不考虑一步复制对称性破缺的自旋玻璃相。
The replica extension theory has been developed for the purpose of investigating spin glass systems in the replica symmetry breaking phase. The replica extension theory is a replica theory for a specific sample and has the scheme of the one-step replica symmetry breaking ansatz. In this paper, using the Plefka expansion, we propose the perturbative expansion of Gibbs free energies of Ising systems with the replica extension theory, and we derive the explicit form of the second-and third-order approximations. Our Plefka expansion systematically provides perturbative approximations taking the one-step replica symmetry breaking into account. In some numerical experiments, we show that our perturbative approximations are quantitatively superior to conventional perturbative approximations that do not take the one-step replica symmetry breaking into account in the spin glass phase.