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

Entropy (Basel). 2019 Feb 5;21(2):153. doi: 10.3390/e21020153.

Authors

Damien Foster¹, Ralph Kenna¹, Claire Pinettes²

Affiliations

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.

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: complex zeros; critical exponents; frustration; phase transitions; polymers; self-avoiding walks.