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

Abstract

We consider ${\varphi }^4$ theory with $\varphi (x)\in \mathbb{R}$ 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, $f_{\mathrm{c}}={\lim }_{\hat{\lambda }\to 0}\hat{\lambda }/{\hat{\mu }}_{\mathrm{c}}^2(\hat{\lambda })$ is determined, with a judicious choice of the parameterizations considered. Our final result reads $f_{\mathrm{c}}=11.1097(20{)}_{\mathrm{stat}}(09{)}_{\mathrm{sys}}=11.1097(22{)}_{\mathrm{tot}}$.

Comments: 13 pages, 6 tables, 6 figures