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.

41 pages, 25 figures. New results added

References in corpus (3)

• Observation of Lee-Yang zeros
• Dynamical Singularities of Glassy Systems in a Quantum Quench
• Tropical Limit in Statistical Physics