Randomness Effect on the Temperature Dependence of the Finite Field Magnetization of a One-Dimensional Spin Gapped System

We investigate the temperature dependence of the finite-field magnetization of the S=1/2 bond-alternating XY model in the Random magnetic field along the z-direction having the Lorentzian distribution. The random-averaged free energy can be exactly calculated, which enables us to obtain the thermodynamical quantities. The temperature dependence of the finite-field magnetization shows various behaviors depending on the parameters $\delta$ and $\Gamma$, where $\delta$ and $\Gamma$ are the bond-alternation parameter and the Lorentzian distribution parameter, respectively.