Ferromagnetism in the two-dimensionalt-Jmodel

The occurrance of ferromagnetism for the t-J model on a square lattice is investigated using high-temperature series for the Helmholtz free energy F and the uniform magnetic susceptibility ${\mathrm{\chi }}_0$. For J=0 fourteenth-order series have been calculated for F and ${\mathrm{\chi }}_0$ and we estimate F(T=0) to find the ground-state energy. A region of fully polarized ferromagnetism is found for J<0. A ferrimagnetic region is observed for larger J/t where ${\mathrm{\chi }}_0$ is divergent, but F(T=0) is below that of spinless fermions. Our results do not support Nagaoka’s theorem at a thermodynamic density of holes.