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arXiv · 1711.00945

Partition function zeros of adsorbing Dyck paths

NR Beaton·EJ Janse van Rensburg
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Abstract

The zeros of the size-$n$ partition functions for a statistical mechanical model can be used to help understand the critical behaviour of the model as $n\to\infty$. Here we use weighted Dyck paths as a simple model of two-dimensional polymer adsorption, and study the behaviour of the partition function zeros, particularly in the thermodynamic limit. The exact solvability of the model allows for a precise calculation of the locus of the zeros and the way in which an edge-singularity on the positive real axis is formed. We also show that in the limit $n\to\infty$ the zeros converge on a lima\c{c}on in the complex plane.

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NR Beaton, EJ Janse van Rensburg. 2017-11-02. Partition function zeros of adsorbing Dyck paths. https://doi.org/10.1088/1751-8121%2Faaabcf

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