# Testing the heating method with perturbation theory

## TL;DR

This paper evaluates the heating method for calculating renormalization constants in lattice topological susceptibility by testing it against exact perturbative results in the 2D $O(3)$ model, confirming its accuracy and usefulness.

## Contribution

It provides a validation of the heating method in a controlled setting and demonstrates its capability to accurately determine perturbative coefficients.

## Key findings

- The heating method yields results consistent with exact perturbative calculations.
- The procedure allows precise determination of first perturbative coefficients.
- The test clarifies features and reliability of the heating method.

## Abstract

The renormalization constants present in the lattice evaluation of the topological susceptibility can be non-perturbatively calculated by using the so-called heating method. We test this method for the $O(3)$ non-linear $\sigma$-model in two dimensions. We work in a regime where perturbative calculations are exact and useful to check the values obtained from the heating method. The result of the test is positive and it clarifies some features concerning the method. Our procedure also allows a rather accurate determination of the first perturbative coefficients.