In response to recent chemical attempts to construct higher-spin ladder materials from organic polyradicals, we study the ground-state properties of a wide class of antiferromagnetic spin-1 ladders. Employing various numerical tools, we reveal the rich phase diagram and correct a preceding nonlinear-sigma-model prediction. A variational analysis well interprets the phase competition with particular emphasis on the { \it re-entrant phase boundary} as a function of the rung interaction.
Categories: cond-mat.str-el cond-mat.stat-mech