Rigorous decimation-based construction of ground pure states for spin-glass models on random lattices

A constructive scheme for the determination of pure states in the 3-spins glass model at very low temperature on a random lattice was reported. The scheme was in full agreement with Parisi's one step replica symmetry breaking (RSB) scheme. The analysis of a partial decimation procedure and the statistical properties of its output was used for the proof. The number of ground states (GS) in each state, the distances between the GS, and the number of states were calculated and these corresponded to RSB predictions.