Zeros and amoebas of partition functions

Singular sectors ${\mathcal{Z}}_{\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}}$ (loci of zeros) for real-valued non-positively defined partition functions $\mathcal{Z}$ of $n$ variables are studied. It is shown that ${\mathcal{Z}}_{\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}}$ 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.