Debashish Chowdhury's critical review of more than a thousand papers not only identifies the complexities involved in the theoretical understanding of the real spin glasses but also explains the physical concepts and the mathematical formalisms that have been used successfully in solving the infiniterange model. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. Spin Glasses and Other Frustrated Systems By Debashish Chowdhury PRINCETON UNIVERSITY PRESS Copyright © 1986 World Scientific Publishing Co Pte Ltd. All rights reserved. ISBN: 978-0-691-08461-9 Contents A note for the readers, 1 Real Spin Glass (SG) Materials, SG-Like Materials and SG Models, 1, 2 A Brief History of the Early Theories of SG, 18, 3 SG "Phase Transition": Order Parameters and Mean-Field Theory, 24, 4 Sherrington-Kirkpatrick (SK) Model and the SK Solution, 38, 5 Instability of the SK Solution, 46, 6 Thouless-Anderson-Palmer (TAP) Solution of the SK Model, 52, 7 Parisi Solution of the SK Model and its Stability, 62, 8 Sompolinsky1s Dynamical Solution of the SK Model and its Stability, 68, 9 Ergodicity, Pure States, Ultrametricity, and Fluctuation-Dissipation Theorem, 73, 10 p-Spin Interaction and the Random Energy Model, 89, 11 Separable SG Glass Models, 96, 12 The Spherical Model of SG, 100, 13 MFT of Vector SG: Mixed Phase, 103, 14 Other Long-Ranged Models, 109, 15 Anisotropic Exchange Interactions and SG, 111, 16 Nonlinear Susceptibilities, AT and GT Lines and Scaling Theories, 121, 17 High-Temperature Expansion, Renormalization Group; Upper and Lower Critical Dimensions, 128, 18 Spin Dynamics in Vector SG: Propagating Modes, 137, 19 Spin Dynamics in SG: Relaxational Modes and Critical Dynamics, 149, 20 Frustration, Gauge Invariance, Defects and SG, 162, 21 Is the SG Transition Analogous to the Blocking of Superparamagnetic Clusters?, 174, 22 Is the SG Transition Analogous to Percolation?, 178, 23 Is the SG Transition Analogous to the Localization-Delocalization Transition?, 181, 24 Computer Simulation Studies and "Numerically Exact" Treatment of SG Models, 186, 25 Transport Properties of SG and Sound Attenuation in SG, 203, 26 Miscellaneous Aspects of SG, 211, 27 SG-Like Systems, 231, APPENDICES, Appendix A: SG Systems and the Nature of the Interactions, 278, Appendix B: General Features of the Experimental Results, 283, References, 325, Addendum, 375, CHAPTER 1 REAL SPIN GLASS (SG) MATERIALS, SG-LIKE MATERIALS AND SG MODELS Magnetic systems exhibit various different types of ordering depending on the temperature T, external magnetic field H, etc. (see Hurd 1982 for an elementary introduction). An experimentalist usually identifies a magnetic material as a spin glass (SG) if it exhibits the following characteristic properties: (i) the low-field, low-frequency a.c. susceptibility xa.c. (T) exhibits a cusp at a temperature Tg, the cusp gets flattened in as small a field (H) as 50 Gauss, (a better criterion is the divergence of the nonlinear susceptibility, as we shall see in chapter 16), (ii) no sharp anomaly appears in the specific heat, (iii) below Tg, the magnetic response is history-dependent; viz. the susceptibility measured in a field-cooled sample is higher than that when cooled in zero-field, (iv) below Tg, the remanent magnetization decays very slowly with time, (v) below Tg, a hysteresis curve, laterally shifted from the origin, appears, (vi) below Tg, no magnetic Bragg scattering, chracteristic of long-range order (LRO), is observed in neutron scattering experiments, thereby demonstrating the absence of LRO (vii) susceptibility begins to deviate from the Curie law at temperatures T >> Tg. (see appendix A for a list of the SG materials and appendix B for a summary of the general features of the experimental results). There are several other systems (not necessarily magnetic) which share at least some of the features of SG and hence we shall call these materials SG-like systems (see chapter 27). From the theoretical point of view, the SG materials have two common features: (a) the disorder is "quenched" and (b) the interaction between the spins are in conflict with each other leading to "frustration" (don't worry if you are not familiar with the two terns within quotes, we shall explain these terns in sections 1.2 and 1.3, respectively. 1.1 SG Models: The simplest model for a d-dimensional magnetic system is the Heisenberg Hamiltonian (see Mattis 1981, 1985) [MA