Use of the complex zeros of the partition function to investigate the critical behavior of the generalized interacting self-avoiding trail model

Damien Foster; Ralph Kenna; Claire Pinettes

doi:10.3390/e21020153

Use of the complex zeros of the partition function to investigate the critical behavior of the generalized interacting self-avoiding trail model

Damien Foster^*, Ralph Kenna, Claire Pinettes

^*Corresponding author for this work

School of Informatics and Digital Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

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, ϕ and ϕ_S, are estimated from the scaling behavior of the leading partition function zeros.

Original language	English
Number of pages	14
Journal	Entropy
Volume	21
Issue number	2
DOIs	https://doi.org/10.3390/e21020153
Publication status	Published - 5 Feb 2019

Bibliographical note

Copyright © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Keywords

Complex zeros
Critical exponents
Frustration
Phase transitions
Polymers
Self-avoiding walks

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10.3390/e21020153Licence: CC BY 4.0

Fosteretal_2019_VoR
Copyright © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Final published version, 1.06 MBLicence: CC BY 4.0

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title = "Use of the complex zeros of the partition function to investigate the critical behavior of the generalized interacting self-avoiding trail model",

abstract = "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, ϕ and ϕS, are estimated from the scaling behavior of the leading partition function zeros.",

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AU - Kenna, Ralph

AU - Pinettes, Claire

N1 - Copyright © 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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N2 - 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, ϕ and ϕS, are estimated from the scaling behavior of the leading partition function zeros.

AB - 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, ϕ and ϕS, are estimated from the scaling behavior of the leading partition function zeros.

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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

Abstract

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Keywords

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