Evidence for massless modes in the 'solvable model' of a spin glass

Abstract

Mean-field equations for the long-range spin-glass model are solved numerically for Tc by an iterative technique. The eigenvalue spectrum of the Hessian, delta ²( beta F)/ delta m_i delta m_j, where F is the free energy, appears to extend down to zero, implying that the solution is always on the limit of stability. It is deduced that the trace of the square of the susceptibility matrix is infinite for Tc.