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Entropy 2019, 21(2), 153; https://doi.org/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

1
Fluid and Complex Systems Research Centre, Faculty of Engineering, Environment and Computing, Coventry CV1 5FB, UK
2
Laboratoire de Physique Théorique et Modélisation (CNRS UMR 8089), Université de Cergy-Pontoise, 2 ave A. Chauvin, 95302 Cergy-Pontoise CEDEX, France
*
Author to whom correspondence should be addressed.
Received: 20 December 2018 / Revised: 28 January 2019 / Accepted: 31 January 2019 / Published: 5 February 2019
PDF [1065 KB, uploaded 5 February 2019]

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.
Keywords: self-avoiding walks; phase transitions; complex zeros; critical exponents; polymers; frustration self-avoiding walks; phase transitions; complex zeros; critical exponents; polymers; frustration
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Foster, D.; Kenna, R.; Pinettes, C. Use of the Complex Zeros of the Partition Function to Investigate the Critical Behavior of the Generalized Interacting Self-Avoiding Trail Model. Entropy 2019, 21, 153.

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