The symmetric six-vertex model and the Segre cubic threefold

被引:2
|
作者
Martins, M. J. [1 ]
机构
[1] Univ Fed Sao Carlos, Dept Fis, BR-13565905 Sao Carlos, SP, Brazil
基金
巴西圣保罗研究基金会;
关键词
integrable models; six-vertex model; Segre threefold;
D O I
10.1088/1751-8113/48/33/334002
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
In this paper we investigate the mathematical properties of the integrability of the symmetric six-vertex model towards the view of algebraic geometry. We show that the algebraic variety originated from Baxter's commuting transfer method is birationally isomorphic to a ubiquitous threefold known as Segre cubic primal. This relation makes it possible to present the most generic solution for the Yang-Baxter triple associated to this lattice model. The respective R-matrix and Lax operators are parameterized by three independent affine spectral variables.
引用
收藏
页数:9
相关论文
共 50 条
  • [1] Convergence of the Stochastic Six-Vertex Model to the ASEPStochastic Six-Vertex Model and ASEP
    Amol Aggarwal
    Mathematical Physics, Analysis and Geometry, 2017, 20
  • [2] STOCHASTIC SIX-VERTEX MODEL
    Borodin, Alexei
    Corwin, Ivan
    Gorin, Vadim
    DUKE MATHEMATICAL JOURNAL, 2016, 165 (03) : 563 - 624
  • [3] On Delocalization in the Six-Vertex Model
    Lis, Marcin
    COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2021, 383 (02) : 1181 - 1205
  • [4] On Delocalization in the Six-Vertex Model
    Marcin Lis
    Communications in Mathematical Physics, 2021, 383 : 1181 - 1205
  • [5] Symmetric Functions from the Six-Vertex Model in Half-Space
    Garbali, Alexandr
    de Gier, Jan
    Mead, William
    Wheeler, Michael
    ANNALES HENRI POINCARE, 2024,
  • [6] The six-vertex model on random lattices
    Zinn-Justin, P
    EUROPHYSICS LETTERS, 2000, 50 (01): : 15 - 21
  • [7] Six-vertex model with an frustrated impurity
    Hara, Y
    Hatano, N
    Suzuki, M
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1997, 66 (10) : 3048 - 3052
  • [8] Boundary polarization in the six-vertex model
    Bogoliubov, NM
    Kitaev, AV
    Zvonarev, MB
    PHYSICAL REVIEW E, 2002, 65 (02):
  • [9] Symmetry relations for the six-vertex model
    Watson, GI
    JOURNAL OF STATISTICAL PHYSICS, 1999, 94 (5-6) : 1045 - 1054
  • [10] Complexity classification of the six-vertex model
    Cai, Jin-Yi
    Fu, Zhiguo
    Xia, Mingji
    INFORMATION AND COMPUTATION, 2018, 259 : 130 - 141