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

TL;DR

This paper develops exactly solvable discrete-time dynamical systems from algebraic matrix operations, explores their reduction to 2+1D discrete classical field theories, and links these theories to inhomogeneous 2D statistical physics models.

Contribution

It introduces new algebraic methods for constructing integrable systems and connects discrete dynamical models with classical field theories and statistical physics.

Findings

Construction of exactly solvable discrete-time systems.

Reduction to classical field theory models in 2+1D discrete space.

Connection established between field theories and inhomogeneous 2D statistical models.

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.