The free energy of spherical pure $p$-spin models -- computation from the TAP approach

Understand

We compute the free energy at all temperatures for the spherical pure $p$-spin models from the generalized Thouless-Anderson-Palmer representation.

• This is the first example of a mixed $p$-spin model for which the free energy is computed in the whole replica symmetry breaking phase, without appealing to the famous Parisi formula.