Critical coupling in $\phi_2^4$ theory

TL;DR

This paper investigates the critical coupling and phase transition in two-dimensional  theory, providing precise numerical estimates of the critical parameters and analyzing the transition from symmetric to broken phases.

Contribution

The study determines the critical bare mass for various couplings and introduces a universal scheme for the transition, with high-precision numerical results for the critical ratio.

Findings

Critical bare mass  as a function of coupling 

Universal scheme for phase transition in  theory

Precise estimate of the critical ratio f_c=11.1097(22)

Abstract

We consider $\phi^4$ theory with $\phi(x)\in\mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\hat{\lambda}$ the (negative) critical bare mass $\hat{\mu}_{0\mathrm{c}}^2(\hat{\lambda})$ where the lattice-regularized system changes from the symmetric to the broken phase. Based on these data, the transition to infinite volume and a universal scheme with the renormalized parameter $\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$ is made. Finally, $f_\mathrm{c}=\lim_{\hat{\lambda}\to0}\hat{\lambda}/\hat{\mu}_\mathrm{c}^2(\hat{\lambda})$ is determined, with a judicious choice of the parameterizations considered. Our final result reads $f_\mathrm{c}=11.1097(20)_\mathrm{stat}(09)_\mathrm{sys}=11.1097(22)_\mathrm{tot}$.