Random energy levels and low-temperature expansions for spin glasses

In a previous paper (cond-mat/0106554) we showed the existence of two new zero-temperature exponents (\lambda and \theta') in two dimensional Gaussian spin glasses. Here we introduce a novel low-temperature expansion for spin glasses expressed in terms of the gap probability distributions for successive energy levels. After presenting the numerical evidence in favor of a random-energy levels scenario, we analyze the main consequences on the low-temperature equilibrium behavior. We find that the specific heat is anomalous at low-temperatures c ~ T**\alpha with \alpha=-d/\theta' which turns out to be linear for the case \theta'=-d.