On correlation functions in the perturbed minimal models M(2,2n+1)

TL;DR

This paper analyzes two-point correlation functions in perturbed minimal models, deriving analytical first-order corrections and combining short- and long-distance approaches for comprehensive understanding.

Contribution

It provides the first-order correction formulas for structure functions and combines conformal perturbation theory with form-factor bootstrap to describe correlations at all scales.

Findings

Short- and long-distance expansions match at intermediate scales.

Including descendent operators improves convergence.

The combined approach accurately describes correlations across all lengths.

Abstract

Two-point correlation functions of spin operators in the minimal models ${{\cal M}}_{p,p'}$ perturbed by the field $\Phi_{13}$ are studied in the framework of conformal perturbation theory. The first-order corrections for the structure functions are derived analytically in terms of gamma functions. Together with the exact vacuum expectation values of local operators, this gives the short-distance expansion of the correlation functions. The long-distance behaviors of these correlation functions in the case ${{\cal M}}_{2,2n+1}$ have been worked out using a form-factor bootstrap approach. The results of numerical calculations demonstrate that the short- and long-distance expansions match at the intermediate distances. Including the descendent operators in the OPE drastically improves the convergency region. The combination of the two methods thus describes the correlation functions at all length scales with good precision.