Quantum-classical phase transition of nucleation rate in a one-dimensional uniaxial Heisenberg model with a magnetic field at an arbitrary direction

We study crossover from quantum tunneling to thermal activation of nucleation rate in a one-dimensional uniaxial Heisenberg model with a magnetic field applied at an arbitrary direction. Considering the periodical boundary condition of spatial coordinate, the type of transition depends critically on the length of ferromagnetic chain. In the low barrier limit two different critical parameter values distinguishing the types of transition are obtained for different angles between the direction of magnetic field and the easy axis (pi /2 much less than phi (H) much less than pi and phi (H) = pi).