Quantum statistical metastability for a finite spin

We study quantum-classical escape-rate transitions for uniaxial and biaxial models with finite spins $S=10\mathrm{}$ (such as ${\mathrm{Mn}}_{12}\mathrm{Ac}$ and ${\mathrm{Fe}}_8)$ and $S=100\mathrm{}$ by a direct numerical approach. At second-order transitions the level making a dominant contribution into thermally assisted tunneling changes gradually with temperature whereas at first-order transitions a group of levels is skipped. For finite spins, the quasiclassical boundaries between first- and second-order transitions are shifted, favoring a second-order transition: For ${\mathrm{Fe}}_8$ in zero field the transition should be first order according to a theory with $\overrightarrow{S}\infty ,$ but we show that there are no skipped levels at the transition. Applying a field along the hard axis in ${\mathrm{Fe}}_8$ makes transition the strongest first order. For the same model with $S=100\mathrm{}$ we confirmed the existence of a region where a second-order transition is followed by a first-order transition [X. Martínes Hidalgo and E. M. Chudnovsky, J. Phys.: Condensed Matter 12, 4243 (2000)].