A Self-Averaging “Order Parameter” for the Sherrington-Kirkpatrick Spin Glass Model

Abstract

Following an idea of van Enter and Griffiths, we define a self-averaging parameter for the Sherrington-Kirkpatrick (SK) spin glass which is a self-averaging version of the order parameter introduced by Aizenman, Lebowitz and Ruelle. It is strictly positive at low temperature and zero at sufficiently high temperature. The proof is based on the recent construction of the thermodynamic limit of the free energy by Guerra and Toninelli. We also discuss how our definition compares with various existing definitions of order-parameter like quantities.