Computer simulation of profiles of interfaces between coexisting phases:: Do we understand their finite size effects?

Interfaces between coexisting phases are very common in condensed matter physics, and thus many simulations attempt to characterize their properties, in particular, the interfacial tension and the interfacial profile. However, while theory usually deals with the intrinsic profile, the latter is not a straightforward output of a simulation: The actual profile (observed in simulations and/or experiments!) is broadened by lateral fluctuations. Therefore, in the usual simulation geometry of L x L x L tin three dimensions), where one chooses suitable boundary conditions to stabilize one or two interfaces of (minimal) area L x L, the profile land in particular the interfacial width) depends on both linear dimensions L and D (parallel and perpendicular to the interface). Choosing recent simulations of interfaces between coexisting phases of unmixed binary polymer mixtures as an example, we show that this interfacial broadening is not a small correction, but has pronounced effects; for a reliable data analysis, it is (unfortunately!) necessary to vary L and D over a wide range. We present counterexamples to the widespread belief that for small linear dimensions, the intrinsic profile is straightforwardly recovered and speculate about conditions where this belief may be valid.