Correlation functions of disorder fields and parafermionic currents in Z(N) Ising models

TL;DR

This paper analyzes correlation functions of parafermionic currents and disorder fields in Z(N) symmetric conformal field theories, using conformal perturbation theory and form factors to understand their behavior across scales.

Contribution

It develops a comprehensive approach combining conformal perturbation theory and form factors for Z(N) models, addressing the structure of scaling fields and resonance issues.

Findings

Agreement between small and large scale data for all N

Identification of null vector relations and equations of motion

Resolution of resonance condition problems

Abstract

We study correlation functions of parafermionic currents and disorder fields in the Z(N) symmetric conformal field theory perturbed by the first thermal operator. Following the ideas of Al. Zamolodchikov, we develop for the correlation functions the conformal perturbation theory at small scales and the form factors spectral decomposition at large ones. For all N there is an agreement between the data at the intermediate distances. We consider the problems arising in the description of the space of scaling fields in perturbed models, such as null vector relations, equations of motion and a consistent treatment of fields related by a resonance condition.