非平衡相变(第1卷)
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作者Malte Henkel，Haye Hinrichsen，Sven Lubeck[著]
出版社世界图书出版公司北京公司
ISBN9787519220723
出版时间2017-07
装帧平装
开本其他
定价65元
货号9165764
上书时间2024-09-04
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作者简介
本书的三位作者Henkel,M./Hinrichsen,H./Lübeck,S.是理论物理和数学物理领域的知名学者,他们撰写的2卷集是一套被各国公认的优秀图书.
目录
1 Introduction
Problems
2 Survey of Equilibrium Critical Phenomena
2.1 Phase Transitions in Equilibrium Systems
2.1.1 Notations
2.1.2 Phase Transitions in Ferromagnetic Systems
2.1.3 Power-law Scaling
2.2 Scale-Invariance and Universality
2.2.1 Scale-Invariance
2.2.2 Scaling Functions and Data Collapses
2.2.3 Universality Classes
2.2.4 Experimental Evidence of Universality
2.3 Mean-Field and Renormalisation Group Methods
2.3.1 Mean-Field Theory of Ferromagnetic Systems
2.3.2 Universal Amplitude Ratios
2.3.3 Remarks on Renormalisation-Group Theory
2.3.4 Scaling Laws Induced by Renormalisation-Group Theory
2.3.5 Field-Theory and c-Expansion
2.3.6 Surface Critical Phenomena
2.3.7 Finite-Size Scaling
2.4 Fluctuation-Dissipation Theorem
2.5 From Scale-Invariance to Conformal Invariance
Problems
3 Directed Percolation
3.1 Directed Percolation at First Glance
3.2 Directed Percolation as a Stochastic Process
3.2.1 Basic Scaling Behaviour
3.2.2 Universality and the DP Conjecture
3.2.3 Simple Mean-Field Approximation
3.2.4 Phenomenological Langevin Equation
3.2.5 Update Schemes and Evolution Equations
3.3 Lattice Models of Directed Percolation
3.3.1 Domany-Kinzel Automaton
3.3.2 Contact Process
3.3.3 Pair-Contact Process
3.3.4 Threshold Transfer Process
3.3.5 Ziff-Gulari-Barshad Model
3.3.6 Further Non-equilihrium Phenomena Related to DP
3.4 Experiments Related to Directed Percolation
3.4.1 Experiments Resembling DP Dynamics
3.4.2 Growth Processes Related to DP
3.4.3 Intermittent Turbulence
3.4.4 Discussion
Problems
4 Scaling Properties of Absorbing Phase Transitions
4.1 Scaling in the Steady-State
4.1.1 Order Parameters
4.1.2 Rapidity-Reversal Symmetry of Directed Percolation
4.1.3 The Correlation Lengths ξ⊥ and ξ∣∣
4.1.4 Scale-Invariance
4.1.5 Two-Point Correlation Function in the Steady-State
4.1.6 Empty-Interval Probabilities in the Steady-State
4.1.7 The External Field h
4.1.8 Fluctuations of the Order-Parameter in the Steady-State
4.1.9 Finite-Size Scaling in the Steady-State
4.2 Dynamical Scaling Behaviour
4.2.1 Homogeneously Active Initial State
4.2.2 Pair-Connectedness Function, I
4.2.3 Spreading Profile at Criticality
4.2.4 Clusters Generated from a Single Seed
4.2.5 Properties of Clusters in the Absorbing Phase
4.2.6 Palr-Connectedness Function, II
4.2.7 Response Function
4.2.8 Early-Time Behaviour and Critical Initial Slip
4.2.9 Fractal Initial Conditions
4.2.10 Influence of an External Field
4.2.11 Finite-Size Scaling
4.2.12 Universality of Finite-Size Amplitudes
4.3 Methods of Analysis
4.3.1 Exact Diagonalisation
4.3.2 Yang-Lee and Fisher Zeros
4.3.3 Series Expansion
4.3.4 Field-Theoretical Methods
4.3.5 Methods for Exact Solution
4.3.6 Monte Carlo Simulations
4.3.7 Universal Moment Ratios
4.3.8 Density-Matrix Renormalisation-Group Methods
4.4 Other Critical Properties
4.4.1 Surface Critical Behaviour
4.4.2 Persistence Exponents
Problems
5 Universality Classes Different from Directed Percolation
5.1 Parity-Conserving Universality Class
5.2 Voter Universality Class
5.2.1 The Classical Voter Model
5.2.2 Voter-Type Phase Transitions
5.3 Compact Directed Percolation
5.4 Tricritical Directed Percolation
5.4.1 Mean-Field Approximation of TDP
5.4.2 Numerical Simulations of TDP
5.5 Dynamical Percolation
5.6 Long-Range Interactions
5.6.1 DP with Spatial Levy Flights
5.6.2 DP with Temporal Long-Range Interactions
5.6.3 Other Models with Long-Range Interactions by Levy Flights
5.6.4 Simulating Models with Long-Range Interactions
5.7 Manna Universality Class
5.7.1 Manna Model
5.7.2 Conserved Threshold Transfer Process (CTTP)
5.7.3 Conserved Lattice Gas (CLG) and Other Reaction-Diffusion Processes
5.7.4 Scaling Properties
5.7.5 Relationship Between Absorbing Phase Transitions and Self-Organised Criticality (SOC)
5.7.6 Absorbing Phase Transitions and SOC: Mean-Field Approximation
5.7.7 Relating Critical Exponents of SOC and Absorbing Phase Transitions
5.8 Pair-Contact Process with Diffusion
5.9 First-Order Phase Transitions
5.9.1 Stabilisation by Elimination of Minority Islands
5.9.2 First-Order Transitions in One Spatial Dimension
5.9.3 Impossibility of Discontinuous Phase Transitions in Fluctuating One-Dimensional Systems
5.9.4 Phase Coexistence and Hysteresis Cycles
5.10 Crossover Phenomena
5.10.1 Crossover from DP to TDP
5.10.2 Crossover from DP to CDP
5.10.3 Crossover to Mean-Field Scaling Behaviour
5.11 Quenched Disorder
5.11.1 Temporally Quenched Disorder
5.11.2 Spatially Quenched Disorder
5.12 Attempts of Classification
5.13 Some Open Questions
Problems
Appendices
A Equilibrium Models
A.1 Potts Model
A.2 Clock Model
A.3 Turban Model
A.4 Baxter-Wu Model
A.5 Blume-Capel Model
A.6 XY Model
A.7 O(n) Model
A.8 Double Exchange Model
A.9 Frustrated Spin Models
A.10 Hilhorst-van Leeuven Model
B Scaling Laws for Absorbing Phase Transitions
C Diagonalisation of Time-Evolution Operators
D Langevin Equations and Path Integrals
E Mean-Field Approximations
E.1 Simple Mean-Field/Site Approximation
E.2 Pair-Approximation
E.3 The Hop-Away Mean-Field Approximation
F Finite-Size Scaling Techniques
F.1 Sequences of Finite-Size Estimates
F.2 Sequence Extrapolation
G Numerical Methods
G.1 Simulational Techniques
G.2 Computation of Response Functions
H Fractal Dimensions
Solutions
Frequently Used Symbols
Abbreviations
References
List of tables
List of figures
Index
精彩内容
《非平衡态相变》是一套标准的教科书，全书分为两卷，内容涉及两类非平衡相变理论。第1卷主要包括吸收相变，其中有进入吸收态的相变静力学和相变动力学等。第2卷论述远离平衡张弛行为和老化。全书各章末有习题，书后附有题解。读者对象：物理及相关专业的研究生。
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