与自旋系统相变有关的非稳态时间序列研究

项目名称： 与自旋系统相变有关的非稳态时间序列研究

项目编号： No.11275184

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 陈志

作者单位： 中国科学技术大学

项目金额： 80万元

中文摘要： 相变一般伴随着某些物理量的发散及与尺度无关的标度不变性，因此该物理量的时间序列在相变时总是非稳的。随着近年来统计物理方法作为重要的科学工具应用于各领域，人们发现在很多复杂系统里非稳态时间序列经常出现并描述着系统的本质性质，而经典的统计物理方法并不适用于处理这些序列。为了解决这个问题，很多优秀的新方法已被提出并深刻地改变了人们对这些系统的认识。但很遗憾的是，其中一些方法的应用目前还未很好的反馈到统计物理本身。本项目将以这些方法为基础探索并发展可以用于与相变有关的非稳态时间序列分析的新工具和方法。为此我们将以自旋系统为例，研究由蒙特卡罗模拟获得的某些物理量在相变点附近的非稳态时间序列。我们将专注于研究：1）与相变有关的标度不变性， 探索相变时物理量高阶涨落、多分形参与的可能性；2）以此为基础争取对目前有争议的自旋玻璃系统的物理图像做出更精确的解释。我们的研究将有利于促进相变理论的进一步发展。

中文关键词： 相变；序参量；多分形；q-统计；希尔伯特变换

英文摘要： Phase transitions usually appear with singularities of certain physical quantities and scale invariance where the system has nocharacteristic length. As a result the time series from those physical quantities are always nonstationary when the system is in critical region. In recent years methods from statistical physics have been applied to various fields as an important tool. With these methods people found that in many complex systems nonstationary time series often appear and describe crucial properties of systems. Methods from conventional statistical physics are not suitable to analyze these signals. To solve this, many novel methods have been proposed and have substantially changed the view to these systems. Regretfully, till now the power of these methods has not yet help the advance of statistical physics. In this research we will develop new tools /methods which can be used to analyze the nonstationary time series related phase transitions based on above novel methods. To do this, we consider the spin system as an example and study nonstationary time series of certain physical quantities near phase transitions obtained through Monte Carlo simulations. We will focus on: (1) scale invariance related to phase transitions, exploring higher moments in fluctuations of certain physical quantities near phase tr

英文关键词： phase transition；order parameter；multifractality；q-statistics；Hilbert transform