Efficient Monte Carlo sampling by direct flattening of free energy barriers

Systems undergoing first-order phase transitions are accompanied by free en ergy barriers which separate the free energy minima characterizing the co-e xisting phases. These barriers grows with increasing system size. With conv entional Monte Carlo simulation methods the characteristic time for crossin g the barriers grows exponentially with system size and the system will nec essarily get trapped in one of the free energy minima. In order to escape f rom this trapping, various novel simulation schemes (e.g., multicanonical/m ultimagnetical sampling, entropic sampling and simulated tempering) have be en proposed and successfully applied to model systems. All these methods co mbine an iterative scheme with histogram reweighting techniques. We apply h ere another variant of these methods, which involves the use of shape funct ions, which are added to the model Hamiltonian in order to level out the fr ee 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 barri ers. The basic principles of the method are presented. The easy adaption of the method to different model systems is demonstrated by application to tw o case studies, a multi-state lattice model for phase equilibria in a binar y lipid bilayer, and a two-dimensional lattice gas model which exhibits int erfacial melting, which are known to be notoriously difficult to study by c onventional Monte Carlo methods, The practical aspects of the implementatio n of the method are discussed, The results demonstrate the efficiency and v ersatility of the shape function method, (C) 1999 Elsevier Science B.V. All rights reserved.