Lack of self-averaging in spin glasses

Abstract

The authors show that there are significant sample variations for the probability distribution of the overlap between phases in the Sherrington-Kirkpatrick spin glass model even in the thermodynamic limit. However experimentally observable quantities, such as the magnetisation, energy and Edwards-Anderson (finite time) order parameter take the same value in all samples. The fluctuation-dissipation theorem holds when a sample average is performed but not for each sample separately.