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The computation of interfacial free energies between coexisting phases(e.g.~saturated vapor and liquid) by computer simulation methods is still achallenging problem due to the difficulty of an atomistic identification of aninterface, and due to interfacial fluctuations on all length scales. Theapproach to estimate the interfacial tension from the free energy excess of asystem with interfaces relative to corresponding single-phase systems does notsuffer from the first problem but still suffers from the latter. Considering$d$-dimensional systems with interfacial area $L^{d-1}$ and linear dimension$L_z$ in the direction perpendicular to the interface, it is argued that theinterfacial fluctuations cause logarithmic finite-size effects of order $\ln(L) / L^{d-1}$ and order $\ln (L_z)/L ^{d-1}$, in addition to regularcorrections (with leading order $\text{const}/L^{d-1}$). A phenomenologicaltheory predicts that the prefactors of the logarithmic terms are universal (butdepend on the applied boundary conditions and the considered statisticalensemble). The physical origin of these corrections are the translationalentropy of the interface as a whole, "domain breathing" (coupling ofinterfacial fluctuations to the bulk order parameter fluctuations of thecoexisting domains), and capillary waves. Using a new variant of the ensembleswitch method, interfacial tensions are found from Monte Carlo simulations of$d=2$ and $d=3$ Ising models and a Lennard Jones fluid. The simulation resultsare fully consistent with the theoretical predictions.

Logarithmic Finite-Size Effects on Interfacial Free Energies: Phenomenological Theory and Monte Carlo Studies