The confined-deconfined interface tension, wetting, and the spectrum of the transfer matrix

The reduced tension ${\sigma }_{cd}$ of the interface between the confined and the deconfined phase of $SU(3)$ pure gauge theory is determined from numerical simulations of the first transfer matrix eigenvalues. At $T_c=1\mathrm{/}{L}_t$ we find ${\sigma }_{cd}=0.139(4)T_c^2$ for $L_t=2$. The interfaces show universal behavior because the deconfined-deconfined interfaces are completely wet by the confined phase. The critical exponents of complete wetting follow from the analytic interface solutions of a $\mathbb{Z}(3)$-symmetric ${\mathrm{\Phi }}^4$ model in three dimensions. We find numerical evidence that the confined-deconfined interface is rough.