A numerical study of the pure states of the Sherrington-Kirkpatrick spin glass model-a comparison with Parisi's replica-symmetry-breaking solution

Abstract

The consistency of a physical interpretation of Parisi's (1979, 1980) replica-symmetry-breaking ansatz using the scheme of pure states is examined by means of numerical solutions of the Thouless-Anderson-Palmer (TAP) equations (1977). A good agreement between the result from the TAP theory and from Parisi's replica solution is obtained for the order parameter function and the internal field distribution. To this extent, the static interpretation of Parisi's solution is correct for the Sherrington-Kirkpatrick spin glass model. As a by-product of the evaluation of Parisi's solution it is found that the Parisi-Toulouse hypothesis holds well numerically. Furthermore, a new microscopic projection hypothesis is proposed.