Singular sectors sing (loci of zeros) for real-valued non-positively defined partition functions of n variables are studied. It is shown that sing have a stratified structure where each stratum is a set of certain hypersurfaces in n. The concept of statistical amoeba is introduced and the properties of a family of statistical amoebas are studied. The relation with algebraic amoebas is discussed. Tropical limits of statistical amoebas are considered too. Applications of the concept of statistical amoeba to the analysis of singular sectors for integrable equations and properties of macroscopic systems with multiple equilibria, including frustrated systems, are discussed.
Zeros and amoebas of partition functions
Angelelli M.
;Konopelchenko B.
2018-01-01
Abstract
Singular sectors sing (loci of zeros) for real-valued non-positively defined partition functions of n variables are studied. It is shown that sing have a stratified structure where each stratum is a set of certain hypersurfaces in n. The concept of statistical amoeba is introduced and the properties of a family of statistical amoebas are studied. The relation with algebraic amoebas is discussed. Tropical limits of statistical amoebas are considered too. Applications of the concept of statistical amoeba to the analysis of singular sectors for integrable equations and properties of macroscopic systems with multiple equilibria, including frustrated systems, are discussed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
