Integrable systems on the lattice and orthogonal polynomials of discrete variable

TL;DR

This paper explores the use of orthogonal polynomials to solve classical and quantum lattice systems and investigates their connections to continuous models, providing insights into integrable systems on the lattice.

Contribution

It introduces a novel approach linking orthogonal polynomials with integrable lattice systems and their continuous counterparts.

Findings

Orthogonal polynomials effectively solve certain lattice systems.

Connections between discrete lattice models and continuous models are established.

New analytical solutions for classical and quantum lattice systems are presented.

Abstract

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.