Exact form factors in integrable quantum field theories: the scaling Z(N)-Ising model

TL;DR

This paper derives exact form factors and operator relations for the scaling Z(N)-Ising model, revealing unique statistical properties that distinguish it from classical field theories.

Contribution

It provides a general form factor formula for the Z(N)-Ising model and explores the unusual statistics of its fields, which are not linked to classical Lagrangians.

Findings

Exact form factors for local operators are obtained.

Commutation rules for order, disorder, and para-Fermi fields are derived.

The model exhibits unusual statistics not related to classical Lagrangians.

Abstract

A general form factor formula for the scaling Z(N)-Ising model is constructed. Exact expressions for matrix elements are obtained for several local operators. In addition, the commutation rules for order, disorder parameters and para-Fermi fields are derived. Because of the unusual statistics of the fields, the quantum field theory seems to be not related to any classical Lagrangian or field equation.