– The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the free-energy barriers which are visible in the probability density of the Parisi overlap parameter. Assuming that the mean barrier height diverges with the...

We present a new dynamical proof of the Thouless-Anderson-Palmer (TAP) equations for classical Sherrington-Kirkpatrick spin glass at sufficiently high temperature. In our derivation, TAP are simple consequence decay two point correlation functions. The methods can also be used to establish higher order illustrate this by proving suitable bound on three functions from which we derive an analogue

We develop the cavity method for the spherical Sherrington-Kirkpatrick model at high temperature and small external field. As one application, we carry out the second moment computations for the overlap and the magnetization.