  We propose an efficient procedure for determining phase diagrams of systems
that are described by spin models. It consists of combining cluster algorithms
with the method proposed by Sauerwein and de Oliveira where the grand canonical
potential is obtained directly from the Monte Carlo simulation, without the
necessity of performing numerical integrations. The cluster algorithm presented
in this paper eliminates metastability in first order phase transitions
allowing us to locate precisely the first-order transitions lines. We also
produce a different technique for calculating the thermodynamic limit of
quantities such as the magnetization whose infinite volume limit is not
straightforward in first order phase transitions. As an application, we study
the Andelman model for Langmuir monolayers made of chiral molecules that is
equivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained the
phase diagrams in the case where the intermolecular forces favor interactions
between enantiomers of the same type (homochiral interactions). In particular,
we have determined diagrams in the surface pressure versus concentration plane
which are more relevant from the experimental point of view and less usual in
numerical studies.
