Nucleation preexponential in dynamic Ising models at moderately strong fields

A dynamic Ising model on a two-dimensional square lattice with nearest neighbor interactions is considered in the metastable region at low temperatures. A large number of low-energy cluster configurations is identified, and for those configurations a system of kinetic equations is written. Solution is obtained using symbolic computational approaches. This allows one to identify the full expression for the nucleation rate, including the preexponential. The treatment generalizes the earlier study of a different, lattice-gas spin-flip dynamics [V. A. Shneidman and G. M. Nita, Phys. Rev. Lett. 89, 025701 (2002)], for the cases of Glauber and Metropolis dynamics and for a broader region of fields. In addition, connection with the lowest-energy nucleation paths (which can be studied analytically, without computer assistance) is examined.