Joel L. Lebowitz, Cyril Domb0122203151, 9780122203152

The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. As the ideas and techniques of critical phenomena have found new areas of application, the field has moved on from being of specialist interest, to occupy a central place in condensed matter studies. This text is part of a series which provides review articles that can serve as standard references for research workers in the field and for graduate students and others wishing to obtain reliable information in important recent developments.

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Table of contents :
Cover page……Page iii_0001.djvu
Contributors……Page v_0001.djvu
General Preface……Page vii_0001.djvu
Preface to Volume 15……Page ix_0001.djvu
Contents……Page xiii_0001.djvu
Contents of Volumes 1-14……Page xv_0001.djvu
1. W. Selke. Spatially Modulated Structures in Systems with Competing Interactions……Page 001_0001.djvu
1.1 Scope and historical aspects……Page 002_0001.djvu
1.2 Basic definitions……Page 004_0001.djvu
2.1. The FK model: continuum limit……Page 007_0001.djvu
2.2. The FK model: discrete case……Page 014_0001.djvu
2.3. Variants and extensions to higher dimensions……Page 019_0001.djvu
3. Spin models……Page 029_0001.djvu
3.1. The ANNNI model……Page 030_0001.djvu
3.2. Other models with discrete spin variables……Page 042_0001.djvu
3.3. Models with continuous spin variables……Page 051_0001.djvu
4.1. The commensurate-incommensurate transition……Page 057_0001.djvu
4.2. The Lifshitz point……Page 059_0001.djvu
References (with author index)……Page 065_0001.djvu
2. A. M. Khorunzhy, B. A. Khoruzhenko, L. A. Pastur and M. V. Shcherbina. The Large-n Limit in Statistical Mechanics and the Spectral Theory of Disordered Systems……Page 073_0001.djvu
1. Introduction……Page 074_0001.djvu
2. Preliminary discussion……Page 078_0001.djvu
3.1. Free energy……Page 088_0001.djvu
3.2. Random external field……Page 093_0001.djvu
3.3. Random infinite-range interaction……Page 095_0001.djvu
3.4. Random short-range interaction……Page 105_0001.djvu
4.1. Free energy……Page 108_0001.djvu
4.2. Correlation functions……Page 113_0001.djvu
5.2. Random external field……Page 116_0001.djvu
5.3. Random uniaxial model……Page 121_0001.djvu
5.4. General one-site anisotropy……Page 128_0001.djvu
5.5. The Sherrington-Kirkpatrick interaction……Page 133_0001.djvu
6.1. General discussion……Page 137_0001.djvu
6.2. Spherical model with two spherical constraints……Page 142_0001.djvu
6.3. Spherical model in an arbitrary periodic field……Page 150_0001.djvu
6.4. Spherical model on a decorated lattice……Page 159_0001.djvu
2. Preliminary discussion……Page 165_0001.djvu
8.1. Semicircle law……Page 171_0001.djvu
8.2. Improvement of the semicircle law and strong self-averaging property……Page 183_0001.djvu
8.3. Band and diluted random matrices……Page 188_0001.djvu
8.4. Sum of random rank-one projections……Page 197_0001.djvu
9.1. Integrated density of states in the Wegner model……Page 201_0001.djvu
9.2. Limits of infinite radius of interaction and infinite space dimension……Page 206_0001.djvu
9.3. Conductivity in the Wegner model in the large-n limit……Page 210_0001.djvu
9.4. Large-n limit in some continuous models……Page 215_0001.djvu
Appendix A: The infinite range limit of the n-vector model……Page 217_0001.djvu
Appendix B: Deformed Wigner ensemble (Gaussian random part)……Page 225_0001.djvu
Appendix C: Derivation of the moment equations for the deformed Wigner ensemble whose random part has finite third moment……Page 227_0001.djvu
Appendix D: Derivation of (8.2.10)……Page 229_0001.djvu
Appendix E: Diluted matrices……Page 231_0001.djvu
Appendix F: Derivation of (9.1.16)……Page 232_0001.djvu
Appendix G: Large-interaction-radius model……Page 233_0001.djvu
References (with author index)……Page 235_0001.djvu
Subject Index……Page 241_0001.djvu