Abstract:
We investigate stability of solutions of the Sherrington-Kirkparick mean-field model for spin glasses with respect to uniform scalings of extensive variables. Scaling transformations leading to multiplications of the phase space are represented with the so-called real replicas. We demonstrate that the demand of thermodynamic homogeneity of the averaged free energy used within linear response theory (replica symmetric averaging) results in a hierarchical free energy from the Parisi replica-symmetry breaking scheme. Thereby an ansatz-free construction of the Parisi solution is obtained together with stability conditions and a natural interpretation of the order parameters.