Convergence to the ground-state energy in the thermodynamic limit of the Ising model in a strong transverse field

Abstract

For the quantum mechanical Ising model in a strong transverse field we show that the convergence of the ground-state energy per site as the volume goes to infinity has an Ornstein-Zernicke behavior. That is, if the diameter of thed-dimensional lattice is given byL, the absolute value of the difference of the ground-state energy per site and its limit is asymptotically exp(-ξL)L−d/2 for some positive constantξ. We also show that the correlation function has the same behavior. Our results are derived by cluster expansions, using a method of Bricmont and Frohlich which we extend to the quantum mechanical case.