# Conformal perturbation theory

## TL;DR

This paper reviews how to use conformal field theory and bootstrap techniques to calculate physical quantities near a critical point, focusing on perturbations of the 2D Ising model.

## Contribution

It introduces a method to compute correlation functions outside the critical point using conformal data from the critical point, applicable to scale-invariant models.

## Key findings

- Method successfully applied to perturbations of the 2D Ising model.
- Provides a safe way to extend critical correlators beyond the critical point.
- Clarifies the use of conformal bootstrap in non-critical regimes.

## Abstract

Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the experimental data of real systems. In order to compute physical quantities near a critical point one needs to know the model at the critical (conformal) point. In this line, recent progresses in the knowledge of conformal field theories, through the conformal bootstrap, give the hope to get some interesting results also outside of the critical point. In this note we will review and clarify how, starting from the knowledge of the critical correlators, one can calculate in a safe way their behavior outside the critical point. The approach illustrated requires the model to be just scale invariant at the critical point. We will clarify the method by applying it to different kind of perturbations of the $2D$ Ising model.