On the Integrable Structure of the Ising Model

TL;DR

This paper analyzes the integrable structure of the Ising model, deriving the exact spectrum of local integrals of motion in the continuum limit and exploring the flow between UV and IR fixed points using TBA techniques.

Contribution

It provides a detailed derivation of the spectrum of local integrals of motion for the Ising model from lattice to continuum, including excited states and boundary conditions.

Findings

Exact spectrum of local integrals of motion derived

Spectrum flow between UV and IR fixed points analyzed

Virasoro eigenstates expressed with rational coefficients

Abstract

Starting from the lattice $A_3$ realization of the Ising model defined on a strip with integrable boundary conditions, the exact spectrum (including excited states) of all the local integrals of motion is derived in the continuum limit by means of TBA techniques. It is also possible to follow the massive flow of this spectrum between the UV $c=1/2$ conformal fixed point and the massive IR theory. The UV expression of the eigenstates of such integrals of motion in terms of Virasoro modes is found to have only rational coefficients and their fermionic representation turns out to be simply related to the quantum numbers describing the spectrum.