Two-dimensional quantum spill systems with ladder and Plaquette structures

We investigate low-energy properties of two-dimensional quantum spin system s with the ladder and plaquette structures, which are described by a genera lized antiferromagnetic Heisenberg model with both of the bond and spin alt ernations, By exploiting a non-linear sigma model technique and a modified spin wave approach, we evaluate the spin gap and the spontaneous magnetizat ion to discuss the quantum phase transition between the ordered and disorde red slates. We argue how the spin-gapped phase is driven to the antiferroma gnetic phase in the phase diagram.