Crossover from thermal hopping to quantum tunneling in ferromagnetic particle

The crossover from thermal hopping to quantum tunneling is studied. We show that the decay rate Γ with dissipation can accurately be determined near the crossover temperature. Besides considering the Wentzel-Kramers-Brillouin exponent, we also calculate contribution of the fluctuation modes around the saddle point and give an extended account of a previous study of crossover region. We deal with two dangerous fluctuation modes whose contribution cannot be calculated by the steepest descent method and show that higher order couplings between the two dangerous modes need to be taken into consideration.