Stability of the Mezard-Parisi solution for random manifolds
  The eigenvalues of the Hessian associated with random manifolds are constructed for the general case of $R$ steps of replica symmetry breaking. For the Parisi limit $R\to\infty$ (continuum replica symmetry breaking) which is relevant for the manifold dimension $D<2$, they are shown to be non negative. 
D.M.Carlucci, C.De Dominicis, T.Temesvari