Parisi states in a Heisenberg spin-glass model in three dimensions

Having developed a hybrid genetic algorithm, we have studied low-lying excited states of the ±J Heisenberg model in two (d = 2) and three (d = 3) dimensions. We have found evidence of the occurrence of the Parisi states in d = 3 but not in d = 2. That is, in Ld lattices, there exist metastable states with a finite excitation energy of ΔE ∼ O(J) for L → ∞, and energy barriers ΔW between the ground state and those metastable states are ΔW ∼ O(JLθ) with θ > 0 in d 3 but with θ < 0 in d = 2. This finding favours the replica-symmetry-breaking or the trivial-nontrivial scenario of the SG phase over the droplet scenario. (letter to the editor)