Efficient Monte Carlo Sampling by direct flattening of free energy barriers

Systems undergoing first-order phase transitions are accompanied by free energy barriers which separate the free energy minima characterizing the co-existing phases. These barriers grows with increasing system size. With conventional Monte Carlo simulation methods the characteristic time for crossing the barriers grows exponentially with system size and the system will necessarily get trapped in one of the free energy minima.

In order to escape from this trapping, various novel simulation schemes (e.g., multicanonical/multimagnetical sampling, entropic sampling and simulated tempering) have been proposed and successfully applied to model systems. All these methods combine an iterative scheme with histogram reweighting techniques.

We apply here another variant of these methods, which involves the use of shape functions, which are added to the model Hamiltonian in order to level out the free energy barriers. One of the virtues of this approach is the transparent formulation of the common philosophy underlying all the different so-called `non-Boltzmann' simulational schemes devised to overcome free energy barriers.

The basic principles of the method are presented. The easy adaption of the method to different model systems is demonstrated by application to two case studies, a multi-state lattice model for phase equilibria in a binary lipid bilayer, and a two-dimensional lattice gas model which exhibits interfacial melting, which are known to be notoriously difficult to study by conventional Monte Carlo methods.

The practical aspects of the implementation of the method are discussed. The results demonstrate the efficiency and versatility of the shape function method.