Mean-field theories of spin glasses

Abstract

Different kinds of mean-field theories (MFT) of spin glasses (SG) are reviewed. A brief introductory review of major experimental results, which have to be explained theoretically, is presented in the beginning. Marshall-Klein-Brout type random local field theories are described qualitatively. Edwards-Anderson MFT of SG transition is introduced after defining the various relevant order parameters. Almost all the static and dynamic approaches to the solution of the Sherrington-Kirkpatrick model are reviewed in detail. The existence of mixed phase(s) in the MFT of vector SG is examined critically in the light of recent theories and experiments. The existence of macroscopic anisotropy energy in SG and their microscopic origin are mentioned. The upper and lower critical dimensionalities obtained by different authors are enlisted. The concept of frustration and its deeper connection with other branches of human knowledge are indicated. Nonlinear susceptibilities, spin wave and relaxational modes in SG are also reviewed. The two-level-system picture of SG, its physical basis and important consequences are presented. The Tholence-Tournier-Wohlfarth phenomenological cluster model of SG is discussed with a stress on the role of measurement time. SG transition has been described as percolation and localization-delocalization problems. Some special features of the local field distribution in SG are mentioned. Some results of computer simulation on the various models of SG are summarized. The theories of the transport properties of SG are enlisted. Recent trends in the theory of SG are indicated at the end.