We explore a method developed in statistical physics which has been argued to have exponentially small finite-volume effects, in order to determine the critical temperature $T_{\mathrm{c}}$ of pure SU(3) gauge theory close to the continuum limit. The method allows us to estimate the critical coupling ${\beta }_c$ of the Wilson action for temporal extents up to $N_{\tau }\sim 20$ with $\lesssim 0.1\%$ uncertainties. Making use of the scale setting parameters $r_0$ and $\sqrt{t_0}$ in the same range of $\beta$-values, these results lead to the independent continuum extrapolations $T_{\mathrm{c}}{r}_0=0.7457(45)$ and $T_{\mathrm{c}}\sqrt{t_0}=0.2489(14)$, with the latter originating from a more convincing fit. Inserting a conversion of $r_0$ from literature (unfortunately with much larger errors) yields $T_{\mathrm{c}}/{\mathrm{\Lambda }}_{\overline{\mathrm{MS}}}=1.24(10)$.

• Received 25 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.096002