Convergence of the free energy of vector spin glasses with non-convex interactions

Source abstract

We prove that the enriched free energy of vector spin glasses converges as the number of sites tends to infinity. The interaction is not assumed to be convex. This is the convergence assumed by Chen and Mourrat (Probab. Math. Phys., 2025) in their representation of the limit as a critical point representation, so that representation holds without further assumptions.