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