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We propose an efficient procedure for determining phase diagrams of systemsthat are described by spin models. It consists of combining cluster algorithmswith the method proposed by Sauerwein and de Oliveira where the grand canonicalpotential is obtained directly from the Monte Carlo simulation, without thenecessity of performing numerical integrations. The cluster algorithm presentedin this paper eliminates metastability in first order phase transitionsallowing us to locate precisely the first-order transitions lines. We alsoproduce a different technique for calculating the thermodynamic limit ofquantities such as the magnetization whose infinite volume limit is notstraightforward in first order phase transitions. As an application, we studythe Andelman model for Langmuir monolayers made of chiral molecules that isequivalent to the Blume-Emery-Griffiths spin-1 model. We have obtained thephase diagrams in the case where the intermolecular forces favor interactionsbetween enantiomers of the same type (homochiral interactions). In particular,we have determined diagrams in the surface pressure versus concentration planewhich are more relevant from the experimental point of view and less usual innumerical studies.

Obtaining pressure versus concentration phase diagrams in spin systems from Monte Carlo simulations