Non-integrable Quantum Field Theories as Perturbations of Certain Integrable Models

TL;DR

This paper develops a perturbative approach to analyze non-integrable 2D quantum field theories by leveraging known properties of integrable models, providing first-order corrections and validating predictions with numerical data.

Contribution

It introduces a method to compute first-order corrections in non-integrable models based on integrable theory data, applied to the Ising model and minimal models.

Findings

First-order mass ratio corrections match numerical data.

Vacuum energy density predictions agree with simulations.

S-matrix modifications are consistent with numerical diagonalization.

Abstract

We approach the study of non--integrable models of two--dimensional quantum field theory as perturbations of the integrable ones. By exploiting the knowledge of the exact $S$-matrix and Form Factors of the integrable field theories we obtain the first order corrections to the mass ratios, the vacuum energy density and the $S$-matrix of the non-integrable theories. As interesting applications of the formalism, we study the scaling region of the Ising model in an external magnetic field at $T \sim T_c$ and the scaling region around the minimal model $M_{2,7}$. For these models, a remarkable agreement is observed between the theoretical predictions and the data extracted by a numerical diagonalization of their Hamiltonian.