Monte Carlo determination of the critical coupling in $\phi^4_2$ theory

TL;DR

This paper employs Monte Carlo simulations on a lattice to non-perturbatively determine the critical coupling in two-dimensional $^4$ theory, providing a precise continuum limit estimate.

Contribution

It presents the first non-perturbative Monte Carlo calculation of the critical coupling in 2D $^4$ theory, refining previous estimates.

Findings

Critical coupling $g/\mu^2=11.15(6)(3)$ in the continuum

Non-perturbative lattice approach applied successfully

Provides benchmark for future theoretical and numerical studies

Abstract

We use lattice formulation of $\phi^4$ theory in order to investigate non--perturbative features of its continuum limit in two dimensions. In particular, by means of Monte Carlo calculations, we obtain the critical coupling constant $g/\mu^2$ in the continuum, where $g$ is the {\em unrenormalised} coupling. Our final result is $g/\mu^2=11.15(6)(3)$.