Speaker
Description
We study the (weak) triviality of the Ising Sherrington-Kirkpatrick TAP energy in the high temperature regime, up to the AT line. Applying the Kac-Rice formula and large deviation techniques, we obtain a variational formula for the TAP complexity of the form sup(q,A)∈[0,1]×R G(q, A) for certain function G(q, A).
For any β and h, we consider the solution (q∗, A∗) of the usual fixed point equa- tion for this model. We prove that (q∗, A∗) is a local maximum of the complexity function G(q, A) up to the AT line, and G(q∗, A∗) = 0.
Moreover, we prove that for β and h satisfying the AT condition the global maximum of G(q, A) is located in a compact set around (q∗, A∗). Hereupon, for many combinations of β, h up to the AT line, we check numerically that that the global maximum in the compact set is indeed (q∗, A∗), confirming that the TAP complexity is 0.
Joint work with David Belius and Giuseppe Genovese.
