An alternate model for magnetization plateaus in the molecular magnet $V_{15}$

Starting from an antiferromagnetic Heisenberg Hamiltonian for the 15 spin-1/2 ions in $V_{15}$, we construct an effective spin Hamiltonian involving eight low-lying states (spin-1/2 and spin-3/2) coupled to a phonon bath. We numerically solve the time-dependent Schrodinger equation of this system, and obtain the magnetization as a function of temperature in a time-dependent magnetic field. The magnetization exhibits unusual patterns of hysteresis and plateaus as the field sweep rate and temperature are varied. The observed plateaus are not due to quantum tunnelling but are a result of thermal averaging. Our results are in good agreement with recent experimental observations