Thouless.Anderson.Palmer equations for generic p-spin glasses.

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, ....,N. We show that the TAP equations hold for the spin at any site with respect to ....,N simultaneously for all .. This result holds for generic models provided that the Parisi measure of the model has a jump at the top of its support.