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

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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, $\phi$ and $\phi_S$, are estimated from the scaling behavior of the leading partition function zeros.
Original languageEnglish
Article number153
Number of pages14
JournalEntropy
Volume21
Issue number2
DOIs
Publication statusPublished - 5 Feb 2019

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Bibliographical note

Special issue: Phase Transitions and Critical Phenomena in Frustrated Systems and Thin Films

c 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

  • Self-Avoiding Walks
  • Polymer Models
  • Partition function zeros
  • Phase transitions
  • Self-avoiding walks
  • Polymers
  • Complex zeros
  • Critical exponents
  • Frustration

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)

Cite this

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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, $\phi$ and $\phi_S$, are estimated from the scaling behavior of the leading partition function zeros.",
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