Journal of Statistical Physics, Vol. 34, Nos. 5/6, 1984, p. 871-881.
Recent developments in the theory of spin glasses are discussed. There has been
considerable progress, due to Parisi, Sompolinsky, and others, towards under-
standing the infinite range (mean field) model of Sherrington and Kirkpatrick.
Relaxation times diverge in the thermodynamic limit, and this nonergodic
behavior is now understood to be the cause of earlier difficulties. There has been
less progress in the study of more realistic models with short-range interactions,
but numerical studies have .shown rather clearly the absence of a finite tempera-
ture transition in two dimensions. There is probably no transition in d = 3 either,
though the evidence is tess clearcut, which makes it difficult to understand the
sharpness of the "freezing" observed experimentally. Well below the freezing
temperature ESR and torque measurements have been fairly well explained by a
theory of Henley, Sompolinsky, and Halperin, in which an important ingredient
is anisotropy due to the Dzyloshinsky-Moriya interaction proposed by Fert and
Levy.