The confined-deconfined Interface Tension 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 related to the finite size effects of the first transfer matrix eigenvalues. A lattice simulation of the transfer matrix spectrum at the critical temperature $T_c=1\mathrm{/}{L}_t$ yields ${\sigma }_{cd}=0.139(4)T_c^2$ for $L_t=2$. We found numerical evidence that the deconfined-deconfined domain walls are completely wet by the confined phase, and that the confined-deconfined interfaces are rough.