Determine replica-symmetry-breaking stability and corrections

Determine the de Almeida–Thouless stability of the replica-symmetric saddle points for Models A and C, and compute the resulting replica-symmetry-breaking corrections to their spin-glass phases and retrieval boundaries.

Background

The phase diagrams and capacities for Models A and C are derived under the replica-symmetric ansatz. The paper notes that replica-symmetry breaking is expected to modify the spin-glass phases and low-temperature phase boundaries, although the corrections to retrieval boundaries are known to be small for the classical case and are expected to remain small for higher-order interactions.

A complete treatment therefore requires testing the de Almeida–Thouless stability of the replica-symmetric solutions and calculating one-step replica-symmetry-breaking corrections to the relevant phase boundaries and spin-glass behavior.

References

The de~Almeida--Thouless (AT) stability of the RS saddle points has not been examined, and the spin-glass phases and the low-temperature boundaries acquire corrections from RSB, known to be small for the retrieval boundaries at $k = 2$ and expected to remain so at $k > 2$.

— Phases in a class of associative memories via hidden neurons  (2609.10976 - Ota et al., 10 Sep 2026) in Section Discussion