# Critical Temperature in Weakly Interacting Multicomponent Field Theory

## TL;DR

This paper introduces a self-similar approximation method to accurately calculate the critical temperature in weakly interacting multicomponent field theories, aligning well with Monte Carlo results.

## Contribution

It presents a novel extrapolation technique using self-similar factor approximants for critical temperature calculations in multicomponent field theories.

## Key findings

- Results agree with Monte Carlo simulations
- Method effectively extrapolates series to finite couplings
- Provides a new tool for critical temperature estimation

## Abstract

A method is suggested for calculating the critical temperature in multicomponent field theory with weak interactions. The method is based on self-similar approximation theory allowing for the extrapolation of series in powers of asymptotically small coupling to finite and even infinite couplings. The extrapolation for the critical temperature employs self-similar factor approximants. The found results are in perfect agreement with Monte Carlo simulations.