Solution planting scheme for fully-connected spin glasses

The advent of new specialized hardware designed to tackle spin-glass-like problems on dense graphs has resulted in a renewed interest in planted solutions for spin-glass Hamiltonians. Here we present a method for planting solutions in fully-connected spin-glass systems with tunable hardness. In particular, the hardness of the problems undergoes a complexity transition. Using both analytical and numerical techniques, we characterize the behavior of these new planted systems.