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physica status solidi (b)

Pade approximation method as renormalization group method

E. Praveczki

Published Nov 1, 1979• 0 citations
Publisher

Abstract

Abstract It is shown that the Pade approximation method applied to high temperature series can be regarded as a special renormalization group method. The renormalization group operator is constructured exactly and explicitly.
DOI
10.1002/pssb.2220960146

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Pad\'e-approximant techniques are applied to the high-temperature series for the temperature derivative of the specific heat of the Ising model. This method indicates a critical exponent $\ensuremath{\alpha}$ in the neighborhood of 18\frac{1}{8}81​ for those Pad\'e approximants which yield an estimate of the critical temperature in substantial agreement with that determined from the susceptibility series.
The method of Padé approximants is applied to the high-temperature series for the susceptibility of the Heisenberg and pair-product models. It is concluded that in both cases the susceptibilities diverge as χ 0 ∝|T-T c | -γ , where γ is nearly 43\frac{4}{3}34​ in three dimensions.
In this paper we have presented a general scheme whereby the method of Padé approximants may be applied to the power series expansion of time dependent correlation functions. It has been demonstrated by actual numerical calculations, using the computer simulated results of Berne and Harp [5], that even a few terms in the power series expansion are capable of reproducing the correlation curves to a fairly large extent. It is pointed out that the method can be extended to higher orders without the introduction of fitting parameters, and without violating the time parity requirements of the Liouville equation. In the final analysis the method is a truly microscopic method since it relies on the microscopic hamiltonian, and the underlying principles are very straightforward. The basic requirements are the spectral moments, but we do not need many of these as the Padé approximants are highly convergent.
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