Recent developments in the theory of spin glasses

Abstract

The actual behavior of real spin glass systems bears little resemblance to that computed by the mean field like theories of Edwards, Anderson and Thouless, and Anderson and Palmer. There is no singularity in the specific heat, and there is an anomalous sensitivity to the magnetic field, for example. The reason has long been expected to be much bigger in this case than for conventional ferro- or antiferromagnetics. I will give a simple argument showing that the Heisenberg spin glass (such as Cu-Mn) is at ’’lower critical dimensionality’’, the lowest dimensionality at which fluctuations allow a phase transition to exist. As a result, its nearest relative is the 2-dimensional x-y model recently solved by Kosterlitz, and I will show how similar the real properties of spin glass are to those computed for the x-y model.