2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/81519We investigate the origin of order in the low-lying spectra of many-body systems with random two-body interactions. Contrary to the common belief our study based both on analytical as well as on numerical arguments shows that these are the higher $J$-sectors whose ground states are more orderly than the ones in the J=0-sector. A predominance of J=0 ground states turns out to be the result of putting on together states with different characteristic energy scales from different $J$-sectors.Latex2e-RevTeX, 4 pages, 4 eps figuresNuclear TheoryCondensed MatterChaotic DynamicsQuantum Physicstext