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Physical review. B, Condensed matter

High-temperature dynamics of the Ising model in a transverse field

J. Oitmaa, Michael Plischke, T.A. Winchester

Published Feb 1, 1984• 10 citations
Publisher

Abstract

We derive the moments, at $T=\ensuremath{\infty}$, of the longitudinal spin-spin correlation function of the Ising model in a transverse field. The first 20 moments are obtained for the linear chain, the first 12 moments for the fcc lattice. We use a method of Nickel [J. Phys. C 7, 1719 (1914)] to construct the relaxation function and find excellent agreement with the exact results of Capel and Perk [Physica (Utrecht) 87A, 211 (1977)] in one dimension and extremely good convergence in three dimensions. Our method of analysis provides much better convergence than methods based on truncation of the continued-fraction representation.

DOI
10.1103/physrevb.29.1321

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The molecular-dynamics technique is applied to the study of the classical ($S=\ensuremath{\infty}$) Ising model in a transverse field on a simple-cubic lattice. The results for the longitudinal- and transverse-relaxation shape function are presented for a set of temperatures in the disordered phase at one value of the transverse field. The longitudinal spectra at $T=\ensuremath{\infty}$ and in the critical regime are analyzed via the Mori's continued-fraction expansion and compared with various approximate results within this approach. The relation of the observed central mode to a domain-wall motion is also discussed. However, due to heavy-damping phenomena no well-defined propagating modes are observed in the critical region. Finally, transverse correlation functions are tested against their diffusive character.
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In this article new results are presented for the zero-temperature ground-state properties of the spin-half transverse Ising model on various lattices using three different approximate techniques. These are, respectively, the coupled cluster method, the correlated basis function method, and the variational quantum Monte Carlo method. The methods, at different levels of approximation, are used to study the ground-state properties of these systems, and the results are found to be in excellent agreement both with each other and with results of exact calculations for the linear chain and results of exact cumulant series expansions for lattices of higher spatial dimension. The different techniques used are compared and contrasted in the light of these results, and the constructions of the approximate ground- state wave functions are especially discussed.
We present asymptotically exact results for the real time order parameter correlations of a class of d=1d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1d=1 Ising models in a transverse field at low temperatures ( TTT) on both sides of the quantum critical point. The correlations are a product of a TTT-independent factor determined by quantum effects, and a TTT-dependent relaxation function which comes from a classical theory. We confirm our predictions by a no-free-parameter comparison with numerical studies on the nearest neighbor spin-1/2 model.