Thermally activated escape rates of uniaxial spin systems with transverse field: Uniaxial crossovers

Classical escape rates of uniaxial spin systems are characterized by a prefactor differing from and much smaller than that of the particle problem, since the maximum of the spin energy is attained everywhere on the line of constant latitude: $\theta =\mathrm{const},$ $0<~\phi <~2\pi .$ If a transverse field is applied, a saddle point of the energy is formed, and high, moderate, and low damping regimes (similar to those for particles) appear. Here we present the first analytical and numerical study of crossovers between the uniaxial and other regimes for spin systems. It is shown that there is one HD-Uniaxial crossover, whereas at low damping the uniaxial and LD regimes are separated by two crossovers.