Lattice Integrals of Motion of the Ising Model on the Strip

TL;DR

This paper demonstrates that the transfer matrix of the 2D critical Ising model on a strip can be expressed as a polynomial in a specific variable, with coefficients linked to lattice integrals of motion, revealing algebraic structure.

Contribution

It introduces a reparametrization of Boltzmann weights that expresses the transfer matrix as a polynomial in sc(4u), connecting it to lattice integrals of motion and the Temperley-Lieb algebra.

Findings

Transfer matrix is a polynomial in sc(4u).

Coefficients relate to lattice local integrals of motion.

Connection to Temperley-Lieb algebra established.

Abstract

We consider the 2D critical Ising model on a strip with fixed boundary conditions. It is shown that for a suitable reparametrization of the known Boltzmann weights the transfer matrix becomes a polynomial in the variable $\csc(4u)$, being $u$ the spectral parameter. The coefficients of this polynomial are decomposed on the fixed boundaries Temperley-Lieb Algebra by introducing a lattice version of the Local Integrals of Motion.