The Ising model with a transverse field. II. Ground state properties

For Pt. I see ibid., vol. 4, 2359 (1971). The properties of the Ising model with a transverse field, with the Hamiltonian written H=- Gamma Sigma _iS_i^x-¹/₂ Sigma _i,jJ_ijS_i^zS_j^z, are studied by perturbation expansions at T=0 in the ground state, both below and above the critical field Gamma _C, for an hypercubic lattice and short range interactions. The order parameter (S^z) and the correlation function G=) Sigma _iS_i^z Sigma _jS_j^z) are calculated respectively below and above Gamma _C. The gap in the excitation spectrum is also studied above the critical field. The critical behaviour obtained from these expansions at T=0 is different from that obtained at T finite and is shown to be analogous to the critical behaviour of the Ising model for a lattice with one more dimension.