2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25919We present first numerical studies of the disorder effect on the recently proposed intrinsic spin Hall conductance in a three dimensional (3D) lattice Luttinger model. The results show that the spin Hall conductance remains finite in a wide range of disorder strength, with large fluctuations. The disorder-configuration-averaged spin Hall conductance monotonically decreases with the increase of disorder strength and vanishes before the Anderson localization takes place. The finite-size effect is also discussed.4 pages, 4 figures; the final version appearing in PRLMesoscale and Nanoscale PhysicsDisordered Systems and Neural Networkstext