  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 LxL
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 heatbath 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.
