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Solid State Communications

The truncation of the mori continued fraction for the spectral function in Heisenberg and XY models

M. Drawid, J. W. Halleý

Published Jun 1, 1977• 0 citations
Publisher
DOI
10.1016/0038-1098(77)90813-4

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The spin dynamics of two dimensional XY ferromagnet are reexamined at low temperatures in the framework of the Mori continued fraction formalism using the Gaussian approximation. In this formalism, the terms on denominators for the Laplace transform of the relaxation function R(t) are related to the frequency moments of the relaxation shape function R(q,w). In the Gaussian approximation scheme, we truncate the continued fraction for R(t) on the second stage. Adopting this approximation, we calculated up to the sixth moment. The moments are writing in terms the static spin correlation functions. In the estimation of the fourth and sixth moment at finite temperature, the four and six-spin correlation functions may be approximated by a sum of products of appropriate pair correlation functions(mode-mode decoupling). In this work we calculated the static spin correlation functions for the expressions to the fourth and sixth moments, needed in the study of the dynamics.
We have computed the sequence of memory functions Kn{K}_{n}Kn​(t) and their Laplace transforms, for the one-dimensional Ising model in a transverse field at T=\ensuremath{\infty}. The form of these functions shows explicitly why the Mori continued-fraction approach, with traditional truncation schemes, fails for this model.