Theory and Applications of the Cluster Variation and Path Probability Methods

1. Front Matter

   Pages i-viii

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2. Problems in the Foundation of the Path Probability Method: Path Probability Function and Entropy Production

   • Ryoichi Kikuchi

   Pages 1-20

3. Ising Model and Kinetic Mean Field Theories

   • F. Ducastelle

   Pages 21-35

4. Kinetic Path and Fluctuations Calculated by the Path Probability Method

   • Tetsuo Mohri, Yoichi Ichikawa, Takayuki Nakahara, Tomoo Suzuki

   Pages 37-51

5. Time Development of Fluctuations in the Path Probability Method

   • Koh Wada, Akiyoshi Kawada, Yuki Kabasawa

   Pages 53-80

6. Universal Dynamic Response in Solid Electrolytes: Formalism of the Path Probability Method as Applied to Transport Problems

   • Hiroshi Sato, Anuradha Datta, Takuma Ishikawa

   Pages 81-93

7. Cluster Variational Approach to Non-Equilibrium Lattice Models

   • Makoto Katori

   Pages 95-111

8. Coherent Anomaly Method and its Applications

   • Masuo Suzuki, Miroslav Kolesik

   Pages 113-124

9. Cluster Variation and Cluster Statics

   • Didier de Fontaine

   Pages 125-144

10. Cluster Variation Method, Effective Field Method, and the Method of Integral Equation on the Regular and Random Ising Models

    • Shigetoshi Katsura

    Pages 145-163

11. The Cluster Variation Method, The Cluster Consistency Method, and The Quantum Cluster Variation Method

    • Tohru Morita

    Pages 165-173

12. The Cluster Expansion Method

    • J. M. Sanchez

    Pages 175-185

13. Lattice Models and Cluster Expansions for the Prediction of Oxide Phase Diagrams and Defect Arrangements

    • G. Ceder, P. D. Tepesch, G. D. Garbulsky, A. F. Kohan

    Pages 187-201

14. Diffuse Scattering of Neutrons in Ni3V and Pt3 V: Test of the Gamma Expansion Method Approximation in a Degenerate Case

    • R. Caudron, D. Le Bolloc’h, A. Finel, M. Barrachin

    Pages 203-217

15. Cluster Variation Method Applications to Large Ising Aggregates

    • F. Aguilera-Granja, J. L. Morán-López

    Pages 219-235

16. Thermodynamic Properties of Coherent Interphase Boundaries in fcc Substitutional Alloys

    • Mark Asta

    Pages 237-254

17. Efficient CVM Methods to Study Interphase Boundary Properties

    • Pierre Cenedese, Ryoichi Kikuchi

    Pages 255-271

18. Ordering of Oxygen Atoms in YBa₂Cu₃O_6+x : Long-Range Coulomb Repulsions

    • A. A. Aligia, J. Garcés

    Pages 273-297

19. Application of the CVM Continuous Atomic Displacement Formulation to the Fracture Problem

    • Kin-ichi Masuda-Jindo, Ryoichi Kikuchi, Robb Thomson

    Pages 299-311

20. Cluster Variation Method Calculations in Binary and Ternary bcc or fcc Phases

    • C. Colinet

    Pages 313-340

This volume is a compilation of papers presented at the International Workshop on the Theory and Applications of the Cluster Variation and Path Probability Methods, held in the city of San Juan, Teotihuacan, Mexico, during June 18-22, 1995. The presentations at the workshop provided a state of the art review of the fundamental aspects of the CVM and PPM and their application to a wide range of problems in statistical mechanics and alloy theory. The volume begins with several articles dealing with the study of the kinetics of ordering in Ising sytems and alloys using the PPM and other classical techniques. These articles are followed by the contribution of Professor Masuo Suzuki on the Coherent Anomaly Method which has added a new dimension to mean field theory, and the CVM in particular, in the study of critical phenomena. The remaining of the volume is dedicated to fundamental aspects and specific applications of the CVM in a wide range of subjects ranging from bulk and surface studies to new areas of inquiry such as the problem of image reconstruction. Since the inception by Prof. Ryoichi Kikuchi of the CVM in 1950 and of the PPM in 1966, the latter after a gestation period of approximately six years, the tech­ niques have found wide acceptance in the physics and materials science communities. Both methods are properly regarded as seminal contributions to equilibrium and non­ equilibrium statistical mechanics.

• alloy
• kinetics
• materials science
• probability
• scattering

• Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico

  J. L. Morán-López

• The University of Texas at Austin, Austin, USA

  J. M. Sanchez

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