Lattice two-point functions and conformal invariance

TL;DR

This paper introduces a lattice-based realization of the conformal algebra that reproduces known two-point functions in lattice models like the Ising and spherical models, revealing a hard core absent in continuum theories.

Contribution

It presents a novel lattice realization of the conformal algebra that accurately reproduces two-point functions and uncovers a hard core feature not seen in continuum conformal field theories.

Findings

Agreement with lattice calculations of the 1+1D Ising model

Agreement with lattice calculations of the d-dimensional spherical model

Identification of a hard core in the lattice realization

Abstract

A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this realization. The result is in agreement with explicit lattice calculations of the $(1+1)D$ Ising model and the $d-$dimensional spherical model. A hard core is found which is not present in the continuum. For a semi-infinite lattice, profiles are also obtained.