  Thermal fluctuations of nanomagnets driven by spin-polarized currents are
treated via the Landau-Lifshitz-Gilbert equation generalized to include both
the random thermal noise field and the Slonczewski spin-transfer torque term.
By averaging this stochastic (Langevin) equation over its realizations, the
explicit infinite hierarchy of differential-recurrence relations for
statistical moments (averaged spherical harmonics) is derived for arbitrary
demagnetizing factors and magnetocrystalline anisotropy for the generic
nanopillar model of a spin-torque device comprising two ferromagnetic strata
representing the free and fixed layers and a nonmagnetic conducting spacer all
sandwiched between two ohmic contacts. The influence of thermal fluctuations
and spin-transfer torques on relevant switching characteristics, such as the
stationary magnetization, the magnetization reversal time, etc., is calculated
by solving the hierarchy for wide ranges of temperature, damping, external
magnetic field, and spin-polarized current indicating new spin-torque effects
in the thermally assisted magnetization reversal comprising several orders of
magnitude. In particular, a pronounced dependence of the switching
characteristics on the directions of the external magnetic field and the spin
polarization exists.
