We developed a hybrid genetic algorithm and studied the ground state and low-lying excitations of the ±J Heisenberg model on a three-dimensional L X L X L(L ≤ 11) lattice. Our results suggest occurrence of a Parisi state. That is, there exists a metastable state with a finite energy of ΔE ∼ O(J) in the thermodynamic limit and the energy barrier ΔW between the metastable state and the ground state is ΔW ∝ JLθ with θ ∼ 0.53. Our results also suggest that the energy ΔE of small scale excitations are related to a scale of the excitation V in a similar manner to those of the ferromagnetic model, i.e., ΔE ∝ JL θLVθυ with θL ∼ -4.7 and θυ ∼ 2.0. This fact suggests that similarity exists in the ground state structure between the ±J and the ferromagnetic Heisenberg models, though the spin directions of those two models differ greatly from one another.
|ジャーナル||Physical Review B - Condensed Matter and Materials Physics|
|出版ステータス||Published - 2004 11 1|
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