Critical coupling in ${\phi }_2^4$ theory

We consider ${\phi }^4$ theory with $\phi (x)\in \mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\widehat{\lambda }$ the (negative) critical bare mass ${\widehat{\mu }}_{0\mathrm{c}}^2(\widehat{\lambda })$ 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 ${\widehat{\mu }}_{\mathrm{c}}^2(\widehat{\lambda })$ is made. Finally, $f_{\mathrm{c}}={\lim }_{\widehat{\lambda }\to 0}\widehat{\lambda }\mathrm{/}{\widehat{\mu }}_{\mathrm{c}}^2(\widehat{\lambda })$ is determined, with a judicious choice of the parameterizations considered. Our final result reads $f_{\mathrm{c}}=11.1097(20{)}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}(09{)}_{\mathrm{s}\mathrm{y}\mathrm{s}}=11.1097(22{)}_{\mathrm{t}\mathrm{o}\mathrm{t}}$.