Metastable behavior of the spin-$s$ Ising and Blume-Capel ferromagnets: A Monte Carlo study.

We present an extensive Monte Carlo investigation of the metastable lifetime through the reversal of the magnetization of the spin-$s$ Ising and Blume-Capel models, where $s=\{1/2, 1, 3/2,2,5/2,3,7/2\}$. The mean metastable lifetime (or reversal time) is studied as a function of the applied magnetic field and for both models is found to obey the Becker-D{\"o}ring theory, as was initially developed for the case of the $s=1/2$ Ising ferromagnet within the classical nucleation theory. We have also studied the decay of the metastable volume fraction which nicely follows Avrami's law for all values of $s$ and for both models. For the case of the Blume-Capel model, the integral behavior of the mean metastable lifetime as function of the temperature ($T$) and single-ion anisotropy ($\Delta$) shows a monotonic variation of the surface (reversal surface) in a three-dimensional plot. Interestingly, the reversal surface appears to be insensitive to the $T-\Delta$ phase boundary of the ferromagnetic-paramagnetic transition of the Blume-Capel ferromagne