Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate t...

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Main Authors:	Damien Foster, Ralph Kenna, Claire Pinettes
Format:	Article
Language:	English
Published:	MDPI AG 2019-02-01
Series:	Entropy
Subjects:	self-avoiding walks phase transitions complex zeros critical exponents polymers frustration
Online Access:	https://www.mdpi.com/1099-4300/21/2/153

id	doaj-25a3331fc12e4a5db0c24a917d0a0ca3
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spelling	doaj-25a3331fc12e4a5db0c24a917d0a0ca32020-11-24T20:45:18ZengMDPI AGEntropy1099-43002019-02-0121215310.3390/e21020153e21020153Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail ModelDamien Foster0Ralph Kenna1Claire Pinettes2Fluid and Complex Systems Research Centre, Faculty of Engineering, Environment and Computing, Coventry CV1 5FB, UKFluid and Complex Systems Research Centre, Faculty of Engineering, Environment and Computing, Coventry CV1 5FB, UKLaboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, 2 ave A. Chauvin, 95302 Cergy-Pontoise CEDEX, FranceThe complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, <inline-formula> <math display="inline"> <semantics> <mi>ϕ</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>ϕ</mi> <mi>S</mi> </msub> </semantics> </math> </inline-formula>, are estimated from the scaling behavior of the leading partition function zeros.https://www.mdpi.com/1099-4300/21/2/153self-avoiding walksphase transitionscomplex zeroscritical exponentspolymersfrustration
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Damien Foster Ralph Kenna Claire Pinettes
spellingShingle	Damien Foster Ralph Kenna Claire Pinettes Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model Entropy self-avoiding walks phase transitions complex zeros critical exponents polymers frustration
author_facet	Damien Foster Ralph Kenna Claire Pinettes
author_sort	Damien Foster
title	Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model
title_short	Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model
title_full	Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model
title_fullStr	Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model
title_full_unstemmed	Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model
title_sort	use of the complex zeros of the partition function to investigate the critical behavior of the generalized interacting self-avoiding trail model
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2019-02-01
description	The complex zeros of the canonical (fixed walk-length) partition function are calculated for both the self-avoiding trails model and the vertex-interacting self-avoiding walk model, both in bulk and in the presence of an attractive surface. The finite-size behavior of the zeros is used to estimate the location of phase transitions: the collapse transition in the bulk and the adsorption transition in the presence of a surface. The bulk and surface cross-over exponents, <inline-formula> <math display="inline"> <semantics> <mi>ϕ</mi> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <msub> <mi>ϕ</mi> <mi>S</mi> </msub> </semantics> </math> </inline-formula>, are estimated from the scaling behavior of the leading partition function zeros.
topic	self-avoiding walks phase transitions complex zeros critical exponents polymers frustration
url	https://www.mdpi.com/1099-4300/21/2/153
work_keys_str_mv	AT damienfoster useofthecomplexzerosofthepartitionfunctiontoinvestigatethecriticalbehaviorofthegeneralizedinteractingselfavoidingtrailmodel AT ralphkenna useofthecomplexzerosofthepartitionfunctiontoinvestigatethecriticalbehaviorofthegeneralizedinteractingselfavoidingtrailmodel AT clairepinettes useofthecomplexzerosofthepartitionfunctiontoinvestigatethecriticalbehaviorofthegeneralizedinteractingselfavoidingtrailmodel
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Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model

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