Convergent Perturbation Theory for the lattice $\phi^4$-model

TL;DR

This paper introduces a convergent perturbation theory for the lattice 4-model, addressing divergence issues in standard methods by modifying the initial approximation, and compares results with Monte Carlo simulations.

Contribution

It develops a convergent perturbation series for the lattice 4-model, improving upon traditional asymptotic series methods.

Findings

Convergent series matches Monte Carlo results for 4-model

Demonstrates improved convergence over standard perturbation theory

Provides a new approach for lattice quantum field theories

Abstract

The standard lattice perturbation theory leads to the asymptotic series because of the incorrect interchange of the summation and integration. However, changing the initial approximation of the perturbation theory, one can generate the convergent series. We study the lattice $\phi^4$-model and compare the operator $\langle\phi_n^2\rangle$ calculated using the convergent series and obtained by Monte Carlo simulations.