Characterizing partition functions of the vertex model

Jan Draisma, Dion C. Gijswijt, L. Lovász, Guus Regts, Alexander Schrijver

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

We characterize which graph parameters are partition functions of a vertex model over an algebraically closed field of characteristic 0 (in the sense of [P. de la Harpe, V.F.R. Jones, Graph invariants related to statistical mechanical models: examples and problems, J. Combin. Theory Ser. B 57 (1993) 207-227]).We moreover characterize when the vertex model can be taken so that its moment matrix has finite rank. Basic instruments are the Nullstellensatz and the First and Second Fundamental Theorems of Invariant theory for the orthogonal group.

Original languageEnglish
Pages (from-to)197-206
Number of pages10
JournalJournal of Algebra
Volume350
Issue number1
DOIs
Publication statusPublished - Jan 15 2012

Fingerprint

Vertex Model
Partition Function
Moment Matrix
Graph Invariants
Invariant Theory
Orthogonal Group
Finite Rank
Algebraically closed
Graph in graph theory
Theorem
Model

Keywords

  • First fundamental theorem
  • Graph invariant
  • Invariant theory
  • Orthogonal group
  • Partition function
  • Second fundamental theorem
  • Vertex model

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Characterizing partition functions of the vertex model. / Draisma, Jan; Gijswijt, Dion C.; Lovász, L.; Regts, Guus; Schrijver, Alexander.

In: Journal of Algebra, Vol. 350, No. 1, 15.01.2012, p. 197-206.

Research output: Contribution to journalArticle

Draisma, J, Gijswijt, DC, Lovász, L, Regts, G & Schrijver, A 2012, 'Characterizing partition functions of the vertex model', Journal of Algebra, vol. 350, no. 1, pp. 197-206. https://doi.org/10.1016/j.jalgebra.2011.10.030
Draisma, Jan ; Gijswijt, Dion C. ; Lovász, L. ; Regts, Guus ; Schrijver, Alexander. / Characterizing partition functions of the vertex model. In: Journal of Algebra. 2012 ; Vol. 350, No. 1. pp. 197-206.
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