Introduction To Percolation Theory
Introduction To Percolation Theory
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DOI：
10.1201/9781315274386
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发表时间：
2018-12
期刊：
影响因子：
--
通讯作者：
D. Stauffer;A. Aharony;S. Redner
中科院分区：
文献类型：
--
作者：
D. Stauffer;A. Aharony;S. Redner
第二版序言
第一版序言
引言：森林火灾、分形油田与扩散
什么是逾渗？
森林火灾
油田与分形
无序介质中的扩散
后续内容简介
进一步阅读
团簇数量
逾渗的真相
一维精确解
d维中的小团簇与“动物”（一种组合结构）
贝特晶格的精确解
团簇数量的标度解探讨
团簇数量的标度假设
数值检验
远离临界概率Pc的团簇数量
进一步阅读
团簇结构
团簇周长是真实的周长吗？
团簇半径与分形维度
对标度的另一种视角
阈值处的无穷团簇
进一步阅读
有限尺寸标度与重正化群
有限尺寸标度
小单元重正化
再谈标度
大单元与蒙特卡罗重正化
与几何的联系
进一步阅读
电导率及相关性质
随机电阻网络的电导率
无穷团簇的内部结构
初期无穷团簇上的众多分形维度
多重分形
分形模型
团簇内部结构的重正化群
连续逾渗、瑞士奶酪模型与宽分布
弹性网络
进一步阅读
行走、动力学与量子效应
迷宫中的蚂蚁
概率分布
分形子与超局域化
外壳与外部可及周长
扩散前沿
入侵逾渗
进一步阅读
在热相变中的应用
统计物理学与伊辛模型
低温下的稀磁体
流体液滴描述的历史
零场下伊辛模型的液滴定义
凯尔泰斯方法的问题
应用
有限温度下的稀磁体
自旋玻璃
进一步阅读
总结
数值技术
Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion in disordered media Coming attractions Further reading Cluster Numbers The truth about percolation Exact solution in one dimension Small clusters and animals in d dimensions Exact solution for the Bethe lattice Towards a scaling solution for cluster numbers Scaling assumptions for cluster numbers Numerical tests Cluster numbers away from Pc Further reading Cluster Structure Is the cluster perimeter a real perimeter? Cluster radius and fractal dimension Another view on scaling The infinite cluster at the threshold Further reading Finite-size Scaling and the Renormalization Group Finite-size scaling Small cell renormalization Scaling revisited Large cell and Monte Carlo renormalization Connection to geometry Further reading Conductivity and Related Properties Conductivity of random resistor networks Internal structure of the infinite cluster Multitude of fractal dimensions on the incipient infinite cluster Multifractals Fractal models Renormalization group for internal cluster structure Continuum percolation, Swiss-cheese models and broad distributions Elastic networks Further reading Walks, Dynamics and Quantum Effects Ants in the labyrinth Probability distributions Fractons and superlocalization Hulls and external accessible perimeters Diffusion fronts Invasion percolation Further reading Application to Thermal Phase Transitions Statistical physics and the Ising model Dilute magnets at low temperatures History of droplet descriptions for fluids Droplet definition for the Ising model in zero field The trouble with Kertesz Applications Dilute magnets at finite temperatures Spin glasses Further reading Summary Numerical Techniques