Slow interaction dynamics in the spherical spin-glass model

A surprising physical interpretation of the replica number n was unveiled in the study of the equilibrium properties of the coupled dynamics of fast Ising spins and slow interactions: n is the ratio of the characteristic temperatures of the spin and the interaction systems and can take on any positive or negative real value, depending on the choice of the coupling dynamics. Here we investigate analytically the thermodynamics of the spherical spin-glass model for general n and derive explicit equations for the transition lines separating the replica symmetric, replica symmetry broken and paramagnetic phases.