The Lattice-Continuum Correspondence in the Ising Model

TL;DR

This paper constructs a subalgebra of smooth operators from the lattice Ising model that reproduces the continuum conformal field theory operator product expansions at criticality.

Contribution

It explicitly links lattice operators to continuum fields, demonstrating the lattice-continuum correspondence in the Ising model at criticality.

Findings

Smooth operators reproduce Ising CFT operator product expansions

Explicit construction of continuum candidate operators from lattice

Analytical proof of lattice-continuum correspondence at critical point

Abstract

Starting from the operator algebra of the (1+1)D Ising model on a spatial lattice, this paper explicitly constructs a subalgebra of smooth operators that are natural candidates for continuum fields in the scaling limit. At the critical value of the transverse field, these smooth operators are analytically shown to reproduce the operator product expansions found in the Ising conformal field theory.