A check of a D = 4 field-theoretical calculation using the high-temperature expansion for Dyson's hierarchical model

J.J Godina; Y Meurice; S Niermann

doi:10.1016/S0550-3213(98)00173-4

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A check of a D = 4 field-theoretical calculation using the high-temperature expansion for Dyson's hierarchical model

Journal article

Peer reviewed

A check of a D = 4 field-theoretical calculation using the high-temperature expansion for Dyson's hierarchical model

J.J Godina, Y Meurice and S Niermann

Nuclear physics. B, Vol.519(3), pp.737-755

1998

DOI: 10.1016/S0550-3213(98)00173-4

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https://arxiv.org/pdf/hep-lat/9710016View

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Abstract

We calculate the high-temperature expansion of the two-point function up to order 800 in β. We show that estimations of the critical exponent γ based on asymptotic analysis are not very accurate in the presence of confluent logarithmic singularities. Using a direct comparison between the actual series and the series obtained from a parametrization of the form ( β c − β) − γ (ln( β c t- β) p + r), we show that the errors are minimized for γ = 0.9997 and p = 0.3351, in very good agreement with field-theoretical calculations. We briefly discuss the related questions of triviality and hyperscaling.

Critical exponents

Hierarchical models

High-temperature expansion

Ising models

Renormalization group

Triviality

Details

Title: Subtitle: A check of a D = 4 field-theoretical calculation using the high-temperature expansion for Dyson's hierarchical model
Creators: J.J Godina - University of Iowa
Y Meurice - University of Iowa
S Niermann - University of Iowa
Resource Type: Journal article
Publication Details: Nuclear physics. B, Vol.519(3), pp.737-755
DOI: 10.1016/S0550-3213(98)00173-4
ISSN: 0550-3213
eISSN: 1873-1562
Publisher: Elsevier B.V
Language: English
Date published: 1998
Academic Unit: Physics and Astronomy
Record Identifier: 9984199672202771

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