Monte Carlo simulation of $\phi^4_2$ and $O(N)\phi^4_3$ theories

TL;DR

This paper uses Monte Carlo simulations with a worm algorithm to study non-perturbative features of $^4$ models in 2 and 3 dimensions, determining critical couplings and exploring $O(N)$ extensions.

Contribution

It introduces a Monte Carlo method based on the all-order strong coupling expansion for $^4$ models, providing new non-perturbative results and preliminary insights into higher-dimensional $O(N)$ models.

Findings

Critical coupling in 2D: g/μ² = 11.15 ± 0.06 (stat) ± 0.03 (syst)

Successful application of worm algorithm to $^4$ models

Initial results for 3D $O(2)^4$ model

Abstract

We report lattice simulations of $\phi^4_2$ and $O(N)\,\phi^4$ models, performed by means of a Monte Carlo method based on the all-order strong coupling expansion (worm algorithm). The investigation of the non-perturbative features of the $\phi^4$ continuum limit in two dimensions lead us to the result $g/\mu^2 = 11.15 \pm 0.06_{stat} \pm 0.03_{syst}$ for the critical coupling. Furthermore we present preliminary results for the three-dimensional $O(2)\phi^4\,$ model using the worm algorithm with the extention to $O(N)\phi^4\,$ in $D$ dimensions.