復雜性和臨界狀態(tài)（英文影印版）

定　價：￥45.00

作　者：	（英）克里斯蒂森，（英）莫洛尼著
出版社：	復旦大學出版社
叢編項：
標　簽：	兩性之間

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ISBN：	9787309052022	出版時間：	2006-11-01	包裝：	膠版紙
開本：	16	頁數：	平裝	字數：

內容簡介

　　《復雜性和臨界狀態(tài)》是作者在從2000年開始給倫敦帝國理工學院研究生講授統(tǒng)計力學的講稿基礎上形成的。復雜性是21世紀的重點研究課題之一，而臨界狀態(tài)則是統(tǒng)計物理中已有相當深入研究的一個分支，《復雜性和臨界狀態(tài)》旨在采用統(tǒng)計力學的方法，以滲濾和伊辛模型為范例，討論突破復雜性研究的途徑?！稄碗s性和臨界狀態(tài)》共分3章，第一章講述滲濾現象的研究方法，并就一維、二維滲濾的定義、點陣結構、塊體的大小和數密度、關聯函數、標度函數、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(tǒng)的自由能和配分函數、磁化強度和磁導率、能量和比熱、響應函數、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(tài)。本章從容易想象的所謂“沙堆”模型出發(fā)，討論沙堆崩塌的物理處理方法，從中引入開放系統(tǒng)的平均場理論、二分叉理論和幾率分布的矩分析、定態(tài)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?！稄碗s性和臨界狀態(tài)》每章之后都有專門設計的練習，為了降低解題難度，每道題都細分為很多小題目，使解題思路十分明確。答案可從http：//www.worldscibooks.com/physics/p365.htm/.查找。為了使不同學科的讀者克服數學上的困難，書后的8個附錄把相關的數學知識和物理量都作了補充交代。

作者簡介

　　Kim Christensen，倫敦帝國理工學院（Imperial College London）理論物理教授。1990年于丹麥Arhus大學物理和天文研究所獲得科學碩士。1993年于丹麥Arhus大學物理和天文研究所獲得科學博士。主要研究興趣是外界因素引起非平衡系統(tǒng)復雜性變化的理論和數值研究，涉及統(tǒng)計力學、復雜性、標度不變性實驗現象、自組織臨界狀態(tài)。 Nicholas R.Moloney，倫敦帝國理工學院（Imperial College London）Blackett實驗室教授。

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 Kadanoffs block spin transformation
2.15.2 Kadanoffs block spin and the free energy
2.15.3 Kadanoffs 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 Wilsons 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