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 Fröhlich which we extend to the quantum mechanical case.
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Pokorny, M. Convergence to the ground-state energy in the thermodynamic limit of the Ising model in a strong transverse field. J Stat Phys 73, 345–360 (1993). https://doi.org/10.1007/BF01052764
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DOI: https://doi.org/10.1007/BF01052764