  Driving nanomagnets by spin-polarized currents offers exciting prospects in
magnetoelectronics, but the response of the magnets to such currents remains
poorly understood. We show that an averaged equation describing the diffusion
of energy on a graph captures the low-damping dynamics of these systems. From
this equation we obtain the bifurcation diagram of the magnets, including the
critical currents to induce stable precessional states and magnetization
switching, as well as the mean times of thermally assisted magnetization
reversal in situations where the standard reaction rate theory of Kramers is no
longer valid. These results match experimental observations and give a
theoretical basis for a N\'eel-Brown-type formula with an effective energy
barrier for the reversal times.
