Kim Christensen
伦敦帝国理工学院（Imperial College London）理论物理教授。1990年于丹麦Arhus大学物理和天文研究所获得科学硕士。1993年于丹麦Arhus大学物理和天文研究所获得科学博士。
主要研究兴趣是外界因素引起非平衡系统复杂性变化的理论和数值研究，涉及统计力学、复杂性、标度不变性实验现象、自组织临界状态。
Nicholas R.Moloney
伦敦帝国理工学院（Imperial College London）Blackett实验室教授。
书摘
出版者的话
复旦大学出版社出版英文影印版《研究生教学参考书系》，主要基于以下几点考虑。
1. (新加坡)世界科技出版公司以出版科技专著闻名于世，同我社已有10多年的友好交往。从20世纪90年代以来，尤其是1995年该公司并购了伦敦帝国学院出版社（Imperial College Press）51%的股份（近年已经完成了100%的股份收购）之后，这两大出版机构在潘国驹教授的集中指挥下，充分发挥了编辑学术委员会的职能，使得出书范围不断拓宽，图书层次逐渐丰富，因此从中遴选影印图书的空间更大了，再加上该公司在上海设有办事机构，相关工作人员工作细致，服务周到，给两个单位的合作交流带来极大的便利。
2. 研究生教育是创新人才培养的关键，教材建设直接关系到研究生科学水平的根本。从2003年开始，我社陆续出版了Fudan Series in Graduate Textbooks这套丛书，国内的读者反响很好。但限于作者人力，这套丛书涵盖的学科和门类都严重不足。为此，我们想到再借助国外出版力量，引进一批图书作为硕士研究生的补充教材，（新加坡）世界科技出版公司与我社的合作，恰好提供了这样一个良好的机会。我们从该公司提供的近期书目中，遴选30多本样书，经过专家审读后，最终确定了其中的11种作为首批《研究生教学参考书系》影印出版。这11种图书的作者来自美、英、法、德、加拿大5个国家的10多所高校或研究部门，他们既是相关学科科研的领军人物，又是高年级本科生和研究生教学的杰出教授。各门教材既考虑到深入浅出的认知规律，又突出了前沿学科的具体应用，每本书都有充实的文献资料，有利于读者和研究人员深入探索。这其中6本教材配有习题，还包括一本具有物理背景的人员都需要了解的高级科普读物——《理解宇宙——从夸克到宇宙学》。
3. 为了有利于广大读者和图书管理人员、图书采购销售人员的使用，特请龚少明编审为每本影印书编写出中文内容介绍和作者概况，并由他将preface（序言）全文译成中文。序言是一本书的总纲，它涉及写作要旨、逻辑体系、内容特色和研读指导等等，我们将其译成中文至少有利于读者浏览和选购，避免买书仓促带来的失误，毕竟英语是多数读者的第二种语言。
4. 原版书价格较贵，大大超出读者的购买能力，即使图书馆或大学资料室也会受到经费不足的制约。出版影印本的书价大约只有原价的十分之一，无疑会给需要这些书的研究生和图书馆带来真正的实惠,这也是（新加坡）世界科技出版公司与我们合作的目的之一。
5. 考虑到物理类图书是（新加坡）世界科技出版公司的第一品牌，我们首次引进的11本书，都属大物理的范畴。这一尝试如果得到读者和专家认可，今后再陆续开辟其他学科的影印渠道。
欢迎读者批评指正，并提出有益的建议。
复旦大学出版社
2006年9月
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
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