Microcanonical determination of the interface tension of flat and curved interfaces from Monte Carlo simulations

The investigation of phase coexistence in systems with multi-component order parameters in finite systems is discussed and, as a generic example, Monte Carlo simulations of the two-dimensional q-state Potts model (q = 30) on L x L square lattices (40 <= L <= 100) are presented. It is shown that the microcanonical ensemble is well suited both to find the precise location of the first-order phase transition and to obtain an accurate estimate for the interfacial free energy between coexisting ordered and disordered phases. For this purpose, a microcanonical version of the heat bath algorithm is implemented. The finite size behaviour of the loop in the curve describing the inverse temperature versus energy density is discussed, emphasizing that the extrema do not have the meaning of van der Waals-like 'spinodal points' separating metastable from unstable states, but rather describe the onset of heterophase states: droplet/bubble evaporation/condensation transitions. Thus all parts of these loops, including the parts that correspond to a negative specific heat, describe phase coexistence in full thermal equilibrium. However, the estimates for the curvature-dependent interface tension of the droplets and bubbles suffer from unexpected and unexplained large finite size effects which need further study.