Non-Equilibrium Phase Transitions (eBook)

Volume 1: Absorbing Phase Transitions

Malte Henkel, Haye Hinrichsen, Sven Lubeck (Autoren)

eBook Download: PDF

2008
XIII, 385 Seiten
Springer Netherlands (Verlag)
978-1-4020-8765-3 (ISBN)

Infos

This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 27.11.2008
• Reihe/Serie: Theoretical and Mathematical Physics
• Reihe/Serie: Theoretical and Mathematical Physics
• Zusatzinfo: XIII, 385 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Festkörperphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Thermodynamik
• Themenwelt: Technik
• Schlagworte: Canopus • directed percolation • nonequilibrium phase transitions • numerical simulation • phase transition • phase transitions • phase transitions into absorbing states • phenomenological scaling theory • renormalisation-group • Variance
• ISBN-10: 1-4020-8765-9 / 1402087659
• ISBN-13: 978-1-4020-8765-3 / 9781402087653