Quenched complexity of the mean-field p-spin spherical model with externalmagnetic field

We consider the p-spin spherical spin-glass model in the presence of an ext ernal magnetic field as a general example of a mean-field system where a on e-step replica symmetry breaking (1-RSB) occurs. In this context we compute the complexity of the Thouless-Anderson-Palmer states, performing a quench ed computation. We find what the general connection is between this method and the standard static 1-RSB one, formulating a clear mapping between the parameters used in the two different calculations. A dynamical analysis of the model confirms the validity of our results.