Ferromagnetism in the two-dimensionalt-Jmodel

The behavior of the Drude weight is studied in the small-J/t regime of the t-J model by Lanczos diagonalizations of small clusters with arbitrary boundary conditions and a small number of holes. Although the total spin of the ground state in the J/t{→}0 limit depends strongly on the boundary conditions, the Drude weight exhibits a rather universal behavior and indicates a sharp transition around J/t{~}0.1 for a hole concentration of {~}10%. This crossover is interpreted as a paramagnetic-ferromagnetic transition. For J/t larger than the crossover value, the Drude weight is somehow constant (and reduced by a factor {~}3 compared to the case of free holes), suggesting that coherent transport is almost insensitive to the variation of the antiferromagnetic correlation length. At small J/t (and finite doping), the exact nature of the ferromagnetic phase is still uncertain, since both fully polarized state or spin-polaron gas are found in small clusters depending on the boundaries.