  A method is proposed for determining the line tension, which is the main
physical characteristic of a three-phase contact region, by Monte-Carlo (MC)
simulations. The key idea of the proposed method is that if a three-phase
equilibrium involves a three-phase contact region, the probability distribution
of states of a system as a function of two order parameters depends not only on
the surface tension, but also on the line tension. This probability
distribution can be obtained as a normalized histogram by appropriate MC
simulations, so one can use the combination of histogram analysis and
finite-size scaling to study the properties of a three phase contact region.
Every histogram and results extracted therefrom will depend on the size of the
simulated system. Carrying out MC simulations for a series of system sizes and
extrapolating the results, obtained from the corresponding series of
histograms, to infinite size, one can determine the line tension of the three
phase contact region and the interfacial tensions of all three interfaces (and
hence the contact angles) in an infinite system. To illustrate the proposed
method, it is applied to the three-dimensional ternary fluid mixture, in which
molecular pairs of like species do not interact whereas those of unlike species
interact as hard spheres. The simulated results are in agreement with
expectations.
