A simplified Parisi ansatz

Simone Franchini

Figure 2. Two extreme pictures for the RSB ansatz for L 3. The diagram shows the edges that contribute to the energy in the orthodox MF ansatz, top figure A, where the Hamiltonian operator is diagonal under Gibbs measure, and a situation where the interfaces dominate the total energy, lower figure B. We expect the second option to be much more likely for fully connected models, because in such models the interfaces are overwhelmingly large with respect to the contribution from edges between spins of the same layer.