Coarse-grained Ginzburg-Landau free energy for Lennard-Jones systems

We discuss the application of Monte Carlo methods to the self-consistent ca lculation of a Ginzburg-Landau free energy functional for Lennard-Jones sys tems in three dimensions. Following this discussion, we demonstrate that th e parameters in the coarse-grained free energy can be extracted from a mult ivariate distribution of energies and particle densities which, when suitab ly reweighted, permit one to extrapolate the results to other nearby points in the thermodynamic parameter space. For the purposes of illustration, bo th single-phase and liquid-gas coexistence are considered here with the aim of describing various regions of the phase diagram with a single function and, in doing so, providing a link between atomistic and mesoscopic length scales. (C) 2000 American Institute of Physics. [S0021-9606(00)51833-9].