Algebraic integrable dynamical systems, 2+1-dimensional models in wholly discrete space-time, and inhomogeneous models in 2-dimensional statistical physics

Abstract

This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in 2+1-dimensional wholly discrete space-time, and to connection between those field theories and inhomogoneous models in 2-dimensional statistical physics.

1) Normally, this must be LaTeXed 3 times! (I beg your pardon) 2) your TeX system must include the \special{em: ...} commands to get the pictures properly, 3) even if it does, one figure is missing--you will see an empty space of height about 8 cm, with a caption below it. Please contact the author

References in corpus (4)

• Elliptic solution for modified tetrahedron equations
• Vacuum curves, classical integrable systems in discrete space-time and statistical physics
• Generalized Yang-Baxter Equation
• A Dynamical System Connected with Inhomogeneous 6-Vertex Model

Cited by in corpus (19)

• On Discrete 3-Dimensional Equations Associated with the Local Yang-Baxter Relation
• Functional Tetrahedron Equation
• Tetrahedron and 3D reflection equations from quantized algebra of functions
• Affine Toda field theory as a 3-dimensional integrable system
• Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
• Invariants in Separated Variables: Yang-Baxter, Entwining and Transfer Maps
• Super-tetrahedra and super-algebras
• Functional Relations on Anisotropic Potts Models: from Biggs Formula to the Tetrahedron Equation
• On a two dimensional system associated with the complex of the solutions of the Tetrahedron equation
• Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation
• Solutions of the functional tetrahedron equation connected with the local Yang -- Baxter equation for the ferro-electric
• Integrability of $q$-oscillator lattice model
• Tetrahedron maps, Yang-Baxter maps, and partial linearisations
• Classical integrable field theories in discrete 2+1 dimensional space-time
• Eigenvector and eigenvalue problem for 3D bosonic model
• Discrete nonlinear hyperbolic equations. Classification of integrable cases
• Exact solution for a matrix dynamical system with usual and Hadamard inverses
• Integrability in 3+1 Dimensions: Relaxing a Tetrahedron Relation
• Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations