A Dynamical System Connected with Inhomogeneous 6-Vertex Model
Abstract
A completely integrable dynamical system in discrete time is studied by means of algebraic geometry. The system is associated with factorization of a linear operator acting in a direct sum of three linear spaces into a product of three operators, each acting nontrivially only in a direct sum of two spaces, and the following reversing of the order of factors. There exists a reduction of the system interpreted as a classical field theory in 2+1-dimensional space-time, the integrals of motion coinciding, in essence, with the statistical sum of an inhomogeneous 6-vertex free-fermion model on the 2-dimensional kagome lattice (here the statistical sum is a function of two parameters). Thus, a connection with the ``local'', or ``generalized'', quantum Yang--Baxter equation is revealed.
Cite
@article{arxiv.hep-th/9402043,
title = {A Dynamical System Connected with Inhomogeneous 6-Vertex Model},
author = {I. G. Korepanov},
journal= {arXiv preprint arXiv:hep-th/9402043},
year = {2008}
}
Comments
21 pages