# Matching numerical simulations to continuum field theories: A lattice renormalization study

## TL;DR

This paper introduces a renormalization-based method to accurately connect lattice simulations of nonlinear field theories with their continuum counterparts, especially when coupled to thermal baths, ensuring correct interpretation of results.

## Contribution

A self-consistent renormalization technique is developed to match lattice models to continuum theories, addressing challenges in simulating nonlinear systems with environmental coupling.

## Key findings

- Successful application to symmetry restoration in φ^4 models
- Provides a systematic way to interpret lattice simulation results in continuum limit
- Enhances accuracy of numerical simulations for nonlinear field theories

## Abstract

The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their dynamics. For nonlinear field theories coupled to thermal (or quantum) baths, discrete lattice formulations must be dealt with extreme care if the results of the simulations are to be interpreted in the continuum limit. Using techniques from renormalization theory, a self-consistent method is presented to match lattice results to continuum models. As an application, symmetry restoration in $\phi^4$ models is investigated.