Characterizing partition functions of the vertex model

JOURNAL OF ALGEBRA

卷:350

Article

Draisma, Jan^1,2  Gijswijt, Dion C.^1,3  Laszlo Lovasz⁴  Regts, Guus¹  Schrijver, Alexander^1,5 

[1] CWI, NL-1098 XG Amsterdam, Netherlands

[2] Eindhoven Univ Technol, NL-5600 MB Eindhoven, Netherlands

[3] Leiden Univ, Dept Math, NL-2300 RA Leiden, Netherlands

[4] Eotvos Lorand Univ, Dept Comp Sci, Budapest, Hungary

[5] Univ Amsterdam, Dept Math, NL-1012 WX Amsterdam, Netherlands

关键词: Vertex model;    Partition function;    Graph invariant;    First Fundamental Theorem;    Second Fundamental Theorem;    Invariant theory;    Orthogonal group;   

DOI  :  10.1016/j.jalgebra.2011.10.030

来源: Elsevier

【 摘 要 】

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 Set. 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. (C) 2011 Elsevier Inc. All rights reserved.

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