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

Abstract

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.

References in corpus (4)

• Simulated Tempering: A New Monte Carlo Scheme
• Multicanonical Ensemble: A New Approach to Simulate First-order Phase Transitions
• Finite-Size Scaling at Phase Coexistence
• Finite-Size Scaling on the Ising Coexistence Line

Cited by in corpus (8)

• Comparing parallel and simulated tempering enhanced sampling algorithms at phase transition regimes
• General approach for studying first-order phase transitions at low temperatures
• First-order phase transitions: A study through the parallel tempering method
• Comparing different protocols of temperature selection in the parallel tempering method
• A simple protocol for the probability weights of the simulated tempering algorithm: applications to first-order phase transitions
• Determining efficient temperature sets for the simulated tempering method
• Equivalence between microcanonical methods for lattice models
• Efficient simulated tempering with approximated weights: Applications to first-order phase transitions