A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model

We calculate the high-temperature expansion of the 2-point function up to order 800 in beta. We show that estimations of the critical exponent gamma based on asymptotic analysis are not very accurate in presence of confluent logarithmic singularities. Using a direct comparison between the actual ser...

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Detalles Bibliográficos
Autores principales: Godina, J J, Meurice, Y, Niermann, S M
Lenguaje:eng
Publicado: 1997
Materias:
Particle Physics - Lattice
Acceso en línea:https://dx.doi.org/10.1016/S0550-3213(98)00173-4
http://cds.cern.ch/record/335339
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author Godina, J J
Meurice, Y
Niermann, S M
author_facet Godina, J J
Meurice, Y
Niermann, S M
author_sort Godina, J J
collection CERN
description We calculate the high-temperature expansion of the 2-point function up to order 800 in beta. We show that estimations of the critical exponent gamma based on asymptotic analysis are not very accurate in presence of confluent logarithmic singularities. Using a direct comparison between the actual series and the series obtained from a parametrization of the form (beta_c -beta)^(-gamma) (Ln(beta_c -beta))^p +r), we show that the errors are minimized for gamma =0.9997 and p=0.3351, in very good agreement with field-theoretical calculations. We briefly discuss the related questions of triviality and hyperscaling
id cern-335339
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1997
record_format invenio
spelling cern-3353392019-09-30T06:29:59Zdoi:10.1016/S0550-3213(98)00173-4http://cds.cern.ch/record/335339engGodina, J JMeurice, YNiermann, S MA Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical ModelParticle Physics - LatticeWe calculate the high-temperature expansion of the 2-point function up to order 800 in beta. We show that estimations of the critical exponent gamma based on asymptotic analysis are not very accurate in presence of confluent logarithmic singularities. Using a direct comparison between the actual series and the series obtained from a parametrization of the form (beta_c -beta)^(-gamma) (Ln(beta_c -beta))^p +r), we show that the errors are minimized for gamma =0.9997 and p=0.3351, in very good agreement with field-theoretical calculations. We briefly discuss the related questions of triviality and hyperscalinghep-lat/9710016CERN-TH-97-252IOWA-97-2502oai:cds.cern.ch:3353391997-10-03
spellingShingle Particle Physics - Lattice
Godina, J J
Meurice, Y
Niermann, S M
A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model
title A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model
title_full A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model
title_fullStr A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model
title_full_unstemmed A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model
title_short A Check of a D=4 Field-Theoretical Calculation Using the High-Temperature Expansion for Dyson's Hierarchical Model
title_sort check of a d=4 field-theoretical calculation using the high-temperature expansion for dyson's hierarchical model
topic Particle Physics - Lattice
url https://dx.doi.org/10.1016/S0550-3213(98)00173-4
http://cds.cern.ch/record/335339
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