Partition function of the eight-vertex model with domain wall boundary condition

2009/03/31 by Wen-Li Yang, Yao-Zhong Zhang
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Boundary (topology) #Boundary value problem #Domain (mathematical analysis) #Function (biology) #Partition (number theory) #Partition function (quantum field theory) #Random Matrices and Applications #Square lattice #cond-mat.stat-mech #hep-th #nlin.SI

paper · pdf · doi:10.1063/1.3205448

published as J. Math. Phys. 50 (2009), 083518 · Latex file, 20 pages; V2, references added

arxiv created 2009/04/22 · openalex publication_date 2009/08/01 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We derive the recursive relations of the partition function for the eight-vertex model on an N×N square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.

Citations

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• Higher spin vertex models with domain wall boundary conditions
• Two elliptic height models with factorized domain wall partition functions
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