Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The ground state of the square lattice bilayer quantum antiferromagnet with nearest (J(1)) and next-nearest (J(2)) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling J(3). The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the pales of the biased Pade approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decreases linearly with alpha(= J(2)/J(1)). The spin-gap phase persists down to J(3) = 0 (single layer limit) for 0.45 less than or similar to alpha less than or similar to 0.65. The crossover of the short range order within the disordered phase is also discussed