Correlators in integrable quantum field theory. The scaling RSOS models

TL;DR

This paper investigates the correlation functions in integrable RSOS models within the scaling limit, comparing theoretical predictions with exact results, and explores their relation to other statistical models through perturbed conformal field theory.

Contribution

It provides an explicit computation of correlation functions in RSOS models and links these models to a broader class of statistical models via perturbed conformal field theory.

Findings

Correlation functions computed with two-particle approximation match exact results.

Central charge and scaling dimensions confirm the accuracy of the correlation calculations.

RSOS models, Potts model, and O(n) vector model share a common perturbed conformal field theory description.

Abstract

The study of the scaling limit of two-dimensional models of statistical mechanics within the framework of integrable field theory is illustrated through the example of the RSOS models. Starting from the exact description of regime III in terms of colliding particles, we compute the correlation functions of the thermal, $\phi_{1,2}$ and (for some cases) spin operators in the two-particle approximation. The accuracy obtained for the moments of these correlators is analysed by computing the central charge and the scaling dimensions and comparing with the exact results. We further consider the (generally non-integrable) perturbation of the critical points with both the operators $\phi_{1,3}$ and $\phi_{1,2}$ and locate the branches solved on the lattice within the associated two-dimensional phase diagram. Finally we discuss the fact that the RSOS models, the dilute $q$-state Potts model at and the O(n) vector model are all described by the same perturbed conformal field theory.