Replica analysis of Franz–Parisi potential for sparse systems

We propose a method for calculating the Franz–Parisi potential for spin glass models on sparse random graphs using the replica method under the replica symmetric ansatz. The resulting self-consistent equations have the solution with the characteristic structure of multi-body overlaps, and the self-consistent equations under this solution are equivalent to the one-step replica symmetry breaking (1RSB) cavity equation with Parisi parameter x = 1. This method is useful for the evaluation of transition temperatures of the p-spin model on regular random graphs under a uniform magnetic field. (paper)