Surface tension in finite-temperature quantum chromodynamics

In a first-order phase transition two phases can coexist at the critical point. The surface free energy $\alpha$, associated with the interface separating the two phases, is an important parameter for the phenomenology of nucleation in supercooled matter and, more generally, for the whole dynamics of a system undergoing the phase transition. We report on a calculation of the surface tension in quenched QCD on lattices with volumes $6^2$×12×2, $8^2$×16×2, and ${10}^2$×20×2, as well as on $8^2$×16×4 and ${12}^2$×24×4. Our results have been obtained from a Monte Carlo simulation where one half of the lattice is adiabatically brought from one phase to the other by applying a temperature gradient, and where the variation of free energy is calculated at the same time through the average of the action. For $N_t=2\mathrm{}$ lattices, we find $\frac{\alpha }{T_c^3}=0.23\mathrm{}\left(3\right)\mathrm{} \mathrm{and} 0.28\left(9\right)\mathrm{}$ on $8^2$×16 and ${10}^2$×20 spatial volumes, respectively. On the other hand, the results from lattices with $N_t=4\mathrm{}$ are less well defined and are compatible with a vanishing surface tension. We discuss possible ways to improve the accuracy of the calculation with larger $N_t$. In particular we propose the use of the Wilson action supplemented with external Polyakov fields as a way to enhance the formation of the interface.