Beschreibung:
We study the Thouless–Anderson–Palmer (TAP) equations for spin glasses on the hypercube. First, using a random, approximately ultrametric decomposition of the hypercube, we decompose the Gibbs measure, 〈·〉N, into a mixture of conditional laws, 〈·〉α, N . We show that the TAP equations hold for the spin at any site with respect to 〈·〉α, N simultaneously for all α. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.