On scaling fields in $Z_N$ Ising models

TL;DR

This paper develops a new algebraic framework for understanding the scaling fields in $Z_N$ symmetric models, providing explicit form factors, vacuum expectation values, and correlation functions relevant to perturbed conformal field theories.

Contribution

It introduces a novel free field representation for form factors of perturbed Virasoro primary fields in $Z_N$ models, linking algebraic relations with physical observables.

Findings

Derived algebraic relations between form factors via deformed parafermionic currents

Constructed explicit free field representations for form factors of primary fields

Calculated exact vacuum expectation values and correlation functions

Abstract

We study the space of scaling fields in the $Z_N$ symmetric models with the factorized scattering and propose simplest algebraic relations between form factors induced by the action of deformed parafermionic currents. The construction gives a new free field representation for form factors of perturbed Virasoro algebra primary fields, which are parafermionic algebra descendants. We find exact vacuum expectation values of physically important fields and study correlation functions of order and disorder fields in the form factor and CFT perturbation approaches.