Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to d-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches $|H|/J=2\mathrm{}$ at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approach zero under these conditions. Near $|H|/J=2\mathrm{}$ and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for $|H|/J>\mathrm{}2\mathrm{}$ and one for $|H|/J<\mathrm{}2.\mathrm{}$