Absorbing phase transitions
著者
書誌事項
Absorbing phase transitions
（Theoretical and mathematical physics, . Non-equilibrium phase transitions ; v. 1）
Springer , In association with Canopus Academic Publishing Limited, c2008
- : hbk.
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
"The career structure and funding of the universities [...] currently strongly d- courages academics and faculties from putting any investment into teaching - there are no career or ?nancial rewards in it. This is a great pity, because [...] it is the need toengage indialogue,and to makethings logicaland clear,that istheprimary defence against obscurantism and abstraction. " B. Ward-Perkins, The fall of Rome, Oxford (2005) This is the ?rst volume of a planned two-volume treatise on non-equilibrium phase transitions. While such a topic might sound rather special and a- demic, non-equilibrium critical phenomena occur in much wider contexts than their equilibrium counterparts, and without having to ?ne-tune th- modynamic variables to their 'critical' values in each case. As a matter of fact, most systems in Nature are out of equilibrium. Given that the theme of non-equilibrium phase transitions of second order is wide enough to amount essentially to a treatment of almost all theoretical aspects of non-equilibrium many-body physics, a selection of topics is required to keep such a project within a manageable length. Therefore, Vol.
1 discusses a particular kind of non-equilibrium phase transitions, namely those between an active, ?- tuating state and absorbing states. Volume 2 (to be written by one of us (MH) with M. Pleimling) will be devoted to ageing phenomena.
目次
1 Introduction. Problems.
2 Survey of Equilibrium Critical Phenomena 2.1 Phase Transitions in Equilibrium Systems 2.2 Scale Invariance and Universality 2.3 Mean-field and Renormalisation Group Methods 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 3.3 Lattice Models of Directed Percolation 3.4 Experiments related to Directed Percolation. Problems.
4 Scaling Properties of Absorbing Phase Transitions 4.1 Scaling in the Steady State 4.2 Dynamical Scaling Behaviour 4.3 Methods of Analysis 4.4 Other Critical Properties. Problems.
5 Universality classes different from directed percolation 5.1 Parity-Conserving Universality Class 5.2 Voter Universality Class 5.3 Compact Directed Percolation 5.4 Tricritical Directed Percolation 5.5 Dynamical Percolation 5.6 Long-range Interactions 5.7 Manna Universality Class 5.8 Pair Contact Process with Diffusion 5.9 First-order Phase Transitions 5.10 Crossover Phenomena 5.11 Quenched Disorder. 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 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 On 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. Solutions. Frequently Used Symbols. Abbreviations. References. Index.
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