Logarithmic corrections to scaling in the two dimensional XY-model

Ralph Kenna; A. C. Irving

doi:10.1016/0370-2693(95)00316-D

Logarithmic corrections to scaling in the two dimensional XY-model

Ralph Kenna, A. C. Irving

School of Computing, Electronics and Maths

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Abstract

By expressing thermodynamic functions in terms of the edge and density of Lee-Yang zeroes, we relate the scaling behaviour of the specific heat to that of the zero field magnetic susceptibility in the thermodynamic limit of the XY-model in two dimensions. Assuming that finite-size scaling holds, we show that the conventional Kosterlitz-Thouless scaling predictions for these thermodynamic functions are not mutually compatible unless they are modified by multiplicative logarithmic corrections. We identify these logarithmic corrections analytically in the case of the specific heat and numerically in the case of the susceptibility. The techniques presented here are general and can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.

Original language	English
Pages (from-to)	273–278
Journal	Physics Letters B
Volume	351
Issue number	1-3
DOIs	https://doi.org/10.1016/0370-2693(95)00316-D
Publication status	Published - 25 May 1995

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Bibliographical note

The full text is also available from: http://de.arxiv.org/abs/hep-lat/9501008
NOTICE: This is the author’s version of a work that was accepted for publication in Physics Letters B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published Physics Letters B, [351, 1-3, 1995] DOI 10.1016/0370-2693(95)00316-D

© 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Cite this

Kenna, R., & Irving, A. C. (1995). Logarithmic corrections to scaling in the two dimensional XY-model. Physics Letters B, 351(1-3), 273–278. https://doi.org/10.1016/0370-2693(95)00316-D

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abstract = "By expressing thermodynamic functions in terms of the edge and density of Lee-Yang zeroes, we relate the scaling behaviour of the specific heat to that of the zero field magnetic susceptibility in the thermodynamic limit of the XY-model in two dimensions. Assuming that finite-size scaling holds, we show that the conventional Kosterlitz-Thouless scaling predictions for these thermodynamic functions are not mutually compatible unless they are modified by multiplicative logarithmic corrections. We identify these logarithmic corrections analytically in the case of the specific heat and numerically in the case of the susceptibility. The techniques presented here are general and can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.",

author = "Ralph Kenna and Irving, {A. C.}",

note = "The full text is also available from: http://de.arxiv.org/abs/hep-lat/9501008 NOTICE: This is the author’s version of a work that was accepted for publication in Physics Letters B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published Physics Letters B, [351, 1-3, 1995] DOI 10.1016/0370-2693(95)00316-D {\circledC} 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/",

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N1 - The full text is also available from: http://de.arxiv.org/abs/hep-lat/9501008 NOTICE: This is the author’s version of a work that was accepted for publication in Physics Letters B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published Physics Letters B, [351, 1-3, 1995] DOI 10.1016/0370-2693(95)00316-D © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

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N2 - By expressing thermodynamic functions in terms of the edge and density of Lee-Yang zeroes, we relate the scaling behaviour of the specific heat to that of the zero field magnetic susceptibility in the thermodynamic limit of the XY-model in two dimensions. Assuming that finite-size scaling holds, we show that the conventional Kosterlitz-Thouless scaling predictions for these thermodynamic functions are not mutually compatible unless they are modified by multiplicative logarithmic corrections. We identify these logarithmic corrections analytically in the case of the specific heat and numerically in the case of the susceptibility. The techniques presented here are general and can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.

AB - By expressing thermodynamic functions in terms of the edge and density of Lee-Yang zeroes, we relate the scaling behaviour of the specific heat to that of the zero field magnetic susceptibility in the thermodynamic limit of the XY-model in two dimensions. Assuming that finite-size scaling holds, we show that the conventional Kosterlitz-Thouless scaling predictions for these thermodynamic functions are not mutually compatible unless they are modified by multiplicative logarithmic corrections. We identify these logarithmic corrections analytically in the case of the specific heat and numerically in the case of the susceptibility. The techniques presented here are general and can be used to check the compatibility of scaling behaviour of odd and even thermodynamic functions in other models too.

U2 - 10.1016/0370-2693(95)00316-D

DO - 10.1016/0370-2693(95)00316-D

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JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

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Access to Document

10.1016/0370-2693(95)00316-D

9501008v1