Abstract
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 iSix-1/2 Sigma i,jJijSizSjz, 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 (Sz) and the correlation function G=) Sigma iSiz Sigma jSjz) 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.

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