Critical finite-size corrections for the Sherrington-Kirkpatrick spin glass

Abstract

Starting from the effective Lagrangian of the Sherrington-Kirkpatrick spin glass near the critical temperature the authors investigate the finite-size effects for the free energy and the propagator above and at Tc=1. They perform the calculation going up to the three-loop diagrams. For T to Tc the cubic vertex only gives the leading term, the inclusion of the quartic vertex gives the following terms. The numerical coefficients in these terms are established by the different methods of the partial summation of perturbation series. The comparison with numerical simulations is done.