複雜性和臨界狀態 （英文影印版）

《複雜性和臨界狀態 （英文影印版）》是2006年11月復旦大學出版社出版的圖書。

基本介紹

• 中文名：複雜性和臨界狀態 （英文影印版）
• 出版社：復旦大學出版社
• 書號：7309052021/O.374
• 作者： [英]Kim Christensen Nicholas R.Moloney
• 定價：45 元
• 頁數：408 頁
• 字數：250千字
• 開本：32 開
• 裝幀：平裝
• 出版日期：2006年11月

內容簡介

全書共分3章，第一章講述滲濾現象的研究方法，並就一維、二維滲濾的定義、點陣結構、塊體的大小和數密度、關聯函式、標度函式、臨界指數和實空間重整化群的變換方法等方面都作了詳盡的介紹。第二章的重點是講述二維伊辛模型的相變理論，涉及相互作用自旋系統的自由能和配分函式、磁化強度和磁導率、能量和比熱、回響函式、平均場理論、相變的朗道ˉ京茨堡理論、Widom標度假設、臨界指數和W ilson重整化群論。第三章介紹自組織臨界狀態。本章從容易想像的所謂“沙堆”模型出發，討論沙堆崩塌的物理處理方法，從中引入開放系統的平均場理論、二分叉理論和幾率分布的矩分析、定態出現的條件等。本章還就地震和降雨的預測預報作了定性討論。

圖書目錄

Contents

Preface

1. Percolation

1.1 Introduction

1.1.1 Definition of site percolation

1.1.2 Quantities of interest

1.2 Percolation in d=1

1.2.1 Cluster number density

1.2.2 Average cluster size

1.2.3 Transition to percolation

1.2.4 Correlation function

1.2.5 Critical occupation probability

1.3 Percolation on the Bethe Lattice

1.3.1 Definition of the Bethe lattice

1.3.2 Critical occupation probability

1.3.3 Average cluster size

1.3.4 Transition to percolation

1.3.5 Cluster number density

1.3.6 Correlation function

1.4 Percolation in d=2

1.4.1 Transition to percolation

1.4.2 Average cluster size

1.4.3 Cluster number density- exact

1.4.4 Cluster number density - numerical

1.5 Cluster Number Density- Scaling Ansatz

1.5.1 Scaling function and data collapse

1.5.2 Scaling function and data collapse in d = 1

1.5.3 Scaling function and data collapse on the Bethe lattice

1.5.4 Scaling function and data collapse in d = 2

1.6 Scaling Relations

1.7 Geometric Properties of Clusters

1.7.1 Self-similarity and fractal dimension

1.7.2 Mass of a large but finite cluster at p = pc

1.7.3 Correlation length

1.7.4 Mass of the percolating cluster for p ＞ pc

1.8 Finite-Size Scaling

1.8.1 Order parameter

1.8.2 Average cluster size and higher moments

1.8.3 Cluster number density

1.9 Non-Universal Critical Occupation Probabilities

1.10 Universal Critical Exponents

1.11 Real-Space Renormalisation

1.11.1 Self-similarity and the correlation length

1.11.2 Self-similarity and fixed points

1.11.3 Coarse graining and rescaling

1.11.4 Real-space renormalisation group procedure

1.11.5 Renormalisation in d = 1

1.11.6 Renormalisation in d = 2 on a triangular lattice

1.11.7 Renormalisation in d = 2 on a square lattice

1.11.8 Approximation via the truncation of parameter space

1.12 Summary

Exercises

2. Ising Model

2.1 Introduction

2.1.1 Definition of the Ising model

2.1.2 Review of equilibrium statistical mechanics

2.1.3 Thermodynamic limit

2.2 System of Non-Interacting Spins

2.2.1 Partition function and free energy

2.2.2 Magnetisation and susceptibility

2.2.3 Energy and specific heat

2.3 Quantities of Interest

2.3.1 Magnetisation

2.3.2 Response functions

2.3.3 Correlation length and spin-spin correlation function

2.3.4 Critical temperature and external field

2.3.5 Symmetry breaking

2.4 Ising Model in d = 1

2.4.1 Partition function

2.4.2 Free energy

2.4.3 Magnetisation and susceptibility

2.4.4 Energy and specific heat

2.4.5 Correlation function

2.4.6 Critical temperature

2.5 Mean-Field Theory of the Ising Model

2.5.1 Partition function and free energy

2.5.2 Magnetisation and susceptibility

2.5.3 Energy and specific heat

2.6 Landau Theory of the Ising Model

2.6.1 Free energy

2.6.2 Magnetisation and susceptibility

2.6.3 Specific heat

2.7 Landau Theory of Continuous Phase Transitions

2.8 Ising Model in d = 2

2.8.1 Partition function

2.8.2 Magnetisation and susceptibility

2.8.3 Energy and specific heat

2.8.4 Critical temperature

2.9 Widom Scaling Ansatz

2.9.1 Scaling ansatz for the free energy

2.9.2 Scaling ansatz for the specific heat

2.9.3 Scaling ansatz for the magnetisation

2.9.4 Scaling ansatz for the susceptibility

2.9.5 Scaling ansatz for the spin-spin correlation function

2.10 Scaling Relations

2.11Widom Scaling Form and Critical Exponents in d = 1

2.12 Non-Universal Critical Temperatures

2.13 Universal Critical Exponents

2.14 Ginzburg Criterion

2.15 Real-Space Renormalisation

2.15.1 Kadanoff's block spin transformation

2.15.2 Kadanoff's block spin and the free energy

2.15.3 Kadanoff's block spin and the correlation function

2.15.4 Renormalisation in d = 1

2.15.5 Renormalisation in d = 2 on a square lattice

2.16 Wilson's Renormalisation Group Theory

2.16.1 Coupling space and renormalisation group flow

2.16.2 Self-similarity and fixed points

2.16.3 Basin of attraction of fixed points

2.16.4 RG flow in coupling and configurational space

2.16.5 Universality and RG flow near fixed point

2.16.6 Widom scaling form

2.17 Summary

Exercises

3. Self-Organised Criticality

3.1 Introduction

3.1.1 Sandpile metaphor

3.2 BTW Model in d = 1

3.2.1 Algorithm of the BTW model in d = 1

3.2.2 Transient and recurrent configurations

3.2.3 Avalanche time series

3.2.4 Avalanche-size probability

3.3 Mean-Field Theory of the BTW Model

3.3.1 Random neighbour BTW model

3.3.2 Algorithm of the random neighbour BTW model

3.3.3 Steady state and the average avalanche size

3.4 Branching Process

3.4.1 Branching ratio

3.4.2 Avalanche-size probability - exact

3.4.3 Avalanche-size probability - scaling form

3.5 Avalanche-Size Probability- Scaling Ansatz

3.6 Scaling Relations

3.7 Moment Analysis of Avalanche-Size Probability

3.8 BTW Model in d = 2

3.8.1 Algorithm of the BTW model in d = 2

3.8.2 Steady state and the average avalanche size

3.8.3 Avalanche time series

3.8.4 Avalanche-size probability

3.9 Ricepile Experiment and the Oslo Model

3.9.1 Ricepile experiment

3.9.2 Ricepile avalanche time series

3.9.3 Ricepile avalanche-size probability density

3.9.4 Ricepile modelling

3.9.5 Algorithm of the Oslo model

3.9.6 Transient and recurrent configurations

3.9.7 Avalanche time series

3.9.8 Avalanche-size probability

3.10 Earthquakes and the OFC Model

3.10.1 Earthquake mechanism

3.10.2 Earthquake time series

3.10.3 Earthquake-size frequency

3.10.4 Earthquake modelling

3.10.5 Algorithm of the OFC model

3.10.6 Steady state and the average avalanche size

3.10.7 Avalanche time series

3.10.8 Avalanche-size probability

3.11 Rainfall

3.11.1 Rainfall mechanism

3.11.2 Rainfall time series

3.11.3 Rainfall-size number density

3.12 Summary

Exercises

Appendix A Taylor Expansion

Appendix B Hyperbolic Functions

Appendix C Homogeneous and Scaling Functions

Appendix D Fractals

Appendix E Data Binning

Appendix F Boltzmann Distribution

Appendix G Free Energy

Appendix H Metropolis Algorithm

Bibliography

List of Symbols

Index