Logo - springer
Slogan - springer

Physics - Classical Continuum Physics | Physics of Critical Fluctuations

Physics of Critical Fluctuations

Ivanchenko, Yuli M., Lisyansky, Alexander A.

Original Russian edition published by Nauka

1995, XVI, 390 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$69.99

(net) price for USA

ISBN 978-1-4612-4204-8

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$98.00

(net) price for USA

ISBN 978-0-387-94414-2

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$98.00

(net) price for USA

ISBN 978-1-4612-8695-0

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • About this textbook

Building on Wilson's renormalization group, the authors have developed a unified approach that not only reproduces known results but also yields new results. A systematic exposition of the contemporary theory of phase transitions, the book includes detailed discussions of phenomena in Heisenberg magnets, granular super-conducting alloys, anisotropic systems of dipoles, and liquid-vapor transitions. Suitable for advanced undergraduates as well as graduate students in physics, the text assumes some knowledge of statistical mechanics, but is otherwise self-contained.

Content Level » Graduate

Keywords » Critical Fluctuations - Renormalization group - particles - phase Transition - quantum system - spectra

Related subjects » Classical Continuum Physics - Complexity

Table of contents 

1. Classical Approach.- 1.1 Introduction.- 1.2 Landau Theory.- 1.2.1 The Scalar Order Parameter.- 1.2.2 The Vector Order Parameter.- 1.3 Broken Symmetry and Condensation.- 1.3.1 Bose-Einstein Condensation.- 1.4 Ergodicity.- 1.4.1 Susceptibility.- 1.4.2 The Ergodic Hypothesis.- 1.5 Gaussian Approximation.- 1.5.1 Goldstone Branch of Excitations.- 1.5.2 Correlation Functions.- 1.5.3 Microscopic Scales in Phase Transitions.- 1.6 The Ginzburg Criterion.- 1.6.1 Critical Dimensions.- 1.7 The Scaling Hypothesis.- 1.7.1 Scaling Laws.- 2 The Ginzburg-Landau Functional.- 2.1 Introduction.- 2.2 Classical Systems.- 2.2.1 The Ising Model.- 2.2.2 The Heisenberg Model.- 2.2.3 Interacting Particles.- 2.3 Quantum Systems.- 2.3.1 The Heisenberg Hamiltonian.- 2.3.2 Bose Gas.- 2.3.3 Bose-Einstein Condensation.- 2.3.4 Fermi Gas.- 3 Wilson’s Renormalization Scheme.- 3.1 Introduction.- 3.2 Kadanoff’s Invariance.- 3.3 Wilson’s Theory.- 3.3.1 Derivation of the RG Equation.- 3.3.2 Linearized RG Equation.- 3.3.3 Redundant Eigenvectors.- 3.3.4 Scaling Properties and Critical Exponents.- 3.3.5 Gaussian Fixed Point.- 3.3.6 The Scaling-Field Method.- 3.3.7 ?-Expansion in Scaling Fields.- 4 Field Theoretical RG.- 4.1 Introduction.- 4.2 Perturbation Theory.- 4.2.1 General Definitions.- 4.2.2 Graph Equations for Ø4-Model.- 4.2.3 Rules of Evaluation.- 4.2.4 Regularization.- 4.3 Renormalization.- 4.3.1 Calculus of Divergences.- 4.3.2 Simple Generalizations.- 4.3.3 Multiplicative Group Equations.- 4.3.4 Scaling Properties.- 4.3.5 Differential Group Equations.- 4.4 Scaling Laws.- 4.5 ?-Expansion.- 4.5.1 Addition of Counter-Terms.- 4.5.2 An Alternative Approach.- 4.5.3 Results.- 4.5.4 Correction to Scaling.- 4.5.5 Improvement of Convergence.- 4.6 Expansions at d = 3.- 4.6.1 Comparison of Massive and Massless Theories.- 4.6.2 Experimental Situation.- 4.7 Results of Different Approaches.- 5 Generalized RG Approach.- 5.1 Introduction.- 5.2 Scale Transformations.- 5.2.1 Differential Form of Scale Covariance.- 5.2.2 Two Ways of Utilizing Scale Covariance.- 5.3 Scale Equations.- 5.3.1 Conventional Approach.- 5.3.2 Generalized Approach.- 5.4 RG Equations.- 5.4.1 Conventional Approach.- 5.4.2 Generalized Approach.- 5.4.3 RG as a Characteristic Set of Scale Equations.- 5.5 Applications of Generalized SE.- 5.5.1 Structure of the Correlation Function at the Transition Point.- 5.5.2 Function ?(q) at the Fixed Point.- 5.6 ?-Expansion.- 5.6.1 General Scheme of the Method.- 5.6.2 Solution of Equations.- 5.6.3 Evaluation of the ?-Exponent.- 5.6.4 Evaluation of the v-Exponent.- 5.7 Comparison of Different RG Approaches.- 6 RG Study of Particular Systems.- 6.1 Reduction of the Characteristic Set.- 6.2 The Gaussian Model.- 6.3 The Ø4 Model.- 6.3.1 General Consideration.- 6.3.2 ð(n) Symmetry.- 6.3.3 Cubic Symmetry.- 6.3.4 Interacting Fields.- 6.3.5 Logarithmical Corrections.- 6.4 The Ø4+Ø6-Model.- 6.5 Free Energy in the Critical Region.- 6.5.1 Quatric Form in the Instability Region.- 6.5.2 Cubic Symmetry.- 6.5.3 Interacting Fields.- 7 Competing Interactions.- 7.1 Heisenberg Magnets.- 7.1.1 RG Equations.- 7.1.2 Fixed Points.- 7.1.3 Flow Lines and Phase Diagrams.- 7.2 Bicritical Points in Antiferromagnets.- 7.2.1 Ginzburg-Landau Functional.- 7.2.2 RG Analysis.- 7.2.3 Experimental Data.- 7.3 Dipole Interaction.- 7.3.1 Dipole Hamiltonian.- 7.3.2 RG Analysis.- 7.3.3 Cubic Symmetry.- 7.3.4 Tetragonal Symmetry.- 7.4 Impure Systems.- 7.4.1 Harris’s Criterion.- 7.4.2 The Replica Method.- 7.4.3 RG Analysis.- 7.4.4 Flow Line Runaway.- 7.4.5 Loop Renormalizations.- 7.4.6 Anisotropic Systems.- 7.4.7 Systems with Competing Interactions.- 8 Exactly Solvable Models and RG.- 8.1 Fluctuation Effects in Spherical Model.- 8.1.1 Inhomogeneous Ordering.- 8.1.2 Homogeneous Ordering.- 8.2 Inversion of Phase Transitions.- 8.3 Model with Reduced Interaction.- 8.3.1 General Consideration.- 8.3.2 Critical Exponents. Crossover.- 8.4 First-Order Transitions.- 8.4.1 Cubic Symmetry.- 8.4.2 Interacting Fields.- 8.5 RG and Reduced Interactions.- 8.5.1 The RG Equation for the Model.- 8.5.2 Critical Exponents.- 9 Application to Copper Oxides.- 9.1 Introduction.- 9.2 La2CuO4 Systems.- 9.2.1 The Ginzburg-Landau Functional.- 9.2.2 Mean Field Approximation.- 9.2.3 RG Analysis.- 9.2.4 The Influence of Impurities.- 9.3 Oxygen Ordering in ABa2Cu3O6+x.- 9.3.1 Description of the Model.- 9.3.2 Free Energy.- 9.3.3 Phase Transition.- 9.3.4 Change of Oxygen Concentration.- 9.4 d-Pairing in the Superconducting State.- 9.4.1 RG Approach.- 9.4.2 An Exactly Solvable Model.- 9.4.3 Comparison with RG.- 9.4.4 Conclusion.- A Evaluation of Integrals.- A.1 Gaussian Integral.- A.2 A Typical Diagram.- B Local RG.- B.1 General Consideration.- B.2 Spectral Theorems.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Thermodynamics.