Zeros and amoebas of partition functions

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.

arXiv comment41 pages, 25 figures. New results added

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• Interpretations of Negative Probabilities
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Cited by in corpus (1)

• Tropical limit and the micro-macro correspondence