2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128767A new powerful method to test the stability of the replica symmetric spin glass phase is proposed by introducing a replicon generator function g(v). Exact symmetry arguments are used to prove that its extremum is proportional to the inverse spin glass susceptibility. By the idea of independent droplet excitations a scaling form for g(v) can be derived, whereas it can be exactly computed in the mean field Sherrington-Kirkpatrick model. It is shown by a first order perturbative treatment that the replica symmetric phase is unstable down to dimensions d<6, and the mean field scaling function proves to be very robust. Although replica symmetry breaking is escalating for decreasing dimensionality, a mechanism caused by the infrared divergent replicon propagator may destroy the mean field picture at some low enough dimension.38 pages, 1 figureDisordered Systems and Neural NetworksStatistical MechanicsMathematical Physicstext