# Shaping Lattice through irrelevant perturbation: Ising model

## TL;DR

This paper identifies the leading irrelevant perturbation in the critical square lattice Ising model, providing explicit coupling expressions and matching spectrum corrections with conformal field theory, enhancing understanding of lattice-continuum relations.

## Contribution

It explicitly relates the irrelevant perturbation to anisotropy and computes spectrum corrections, bridging lattice models and conformal field theory with exact agreement.

## Key findings

- Explicit coupling constant in terms of anisotropy
- Exact agreement of spectrum corrections between lattice and CFT
- Relation between perturbing operators and higher integrals of motion

## Abstract

The leading irrelevant perturbation, which controls the deviation of critical square lattice Ising model with periodic boundary conditions from its continuous CFT analog is identified. An explicit expression for the coupling constant in terms of the anisotropy parameter is found. We calculate the next to leading $\sim 1/N^2$ corrections to the spectrum on both lattice theory and the perturbed CFT sides for several classes of states, always getting exact agreement. We discuss also how the perturbing operators and the higher integrals of motion are related.