Critical coupling in $\ddot{I}{•}_2^4$ theory

Abstract

We consider $\ddot{I}{•}^4$ theory with $\ddot{I}•(x)\in \mathbb{R}$ in two Euclidean dimensions. We determine for a variety of self-couplings $\hat{\hat{I}}»$ the (negative) critical bare mass $\hat{\hat{I}}{¼}_{0\mathrm{c}}^2(\hat{\hat{I}}»)$ 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 $\hat{\hat{I}}{¼}_{\mathrm{c}}^2(\hat{\hat{I}}»)$ is made. Finally, $f_{\mathrm{c}}={\lim }_{\hat{\hat{I}}»\to 0}\hat{\hat{I}}»/\hat{\hat{I}}{¼}_{\mathrm{c}}^2(\hat{\hat{I}}»)$ is determined, with a judicious choice of the parameterizations considered. Our final result reads $f_{\mathrm{c}}=11.1097(20{)}_{\mathrm{stat}}(09{)}_{\mathrm{sys}}=11.1097(22{)}_{\mathrm{tot}}$.

13 pages, 6 tables, 6 figures