Studies of phase change in complex systems using the generalized replica exchange method

The replica exchange method (REM) has been widely used in the computer simulation of complex systems, such as proteins, glasses, and atomic clusters, where conventional methods based on sampling the canonical ensemble struggle to attain ergodicity over a rugged energy landscape characterized by multiple minima separated by high energy barriers. While the standard temperature REM (tREM) has proven to be highly effective in the equilibrium sampling of stable single phase states, tREM is seriously challenged in the vicinity of a first-order phase transition. The generalized Replica Exchange Method (gREM) was developed to address these outstanding computational problems and provide a method for simulating strong phase transitions in condensed matter systems. The central idea behind gREM is to incorporate the merit of generalized ensemble sampling into the replica exchange paradigm. The key ingredients of gREM are parameterized effective sampling weights, which smoothly join ordered and disordered phases with a succession of unimodal energy distributions that transform unstable or metastable energy states of the canonical ensemble into stable states that can be fully characterized. The inverse mapping between the sampling weights and the effective v temperature provides a sure way to design the effective sampling weights and achieve ergodic sampling. Various applications of gREM are presented, including studies of the solid-liquid phase change of an adapted Dzugutov model of glass formation, the mechanism of spinodal decomposition in the vapor-liquid transition of a simple fluid, and the apparent crossover from a first-order to continuous transition with increasing density in the freezing of a nanofilm of water confined between featureless and atomistic surfaces. Extensive gREM simulations combined with the Statistical Temperature Weighted Histogram Analysis Method (ST-WHAM) demonstrate the effectiveness of the approach and provide comprehensive characterization of thermodynamic and structural properties intrinsic to phase transitions in these diverse systems.