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arXiv · 1607.05937

Zeros and amoebas of partition functions

M. Angelelli·B. Konopelchenko
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Abstract

Singular sectors $\mathcal{Z}_{\mathrm{sing}}$ (loci of zeros) for real-valued non-positively defined partition functions $\mathcal{Z}$ of $n$ variables are studied. It is shown that $\mathcal{Z}_{\mathrm{sing}}$ have a stratified structure and each stratum is a set of certain hypersurfaces in $\mathbb{R}^n$. The concept of statistical amoebas is introduced and their properties are studied. Relation with algebraic amoebas is discussed. Tropical limit of statistical amoebas is considered too.

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M. Angelelli, B. Konopelchenko. 2016-07-20. Zeros and amoebas of partition functions. https://arxiv.org/abs/1607.05937

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