On the reliability of mean-field methods in polymer statistical mechanics

The reliability of the mean-field approach to polymer statistical mechanics is investigated by comparing results from a recently developed lattice mea n-field theory (LMFT) method to statistically exact results from two indepe ndent numerical Monte Carlo simulations for the problems of a polymer chain moving in a spherical cavity and a polymer chain partitioning between two confining spheres of different radii. It is shown that in some cases the ag reement between the LMFT and the simulation results is excellent, while in others, such as the case of strongly fluctuating monomer repulsion fields, the LMFT results agree with the simulations only qualitatively. Various app roximations of the LMFT method are systematically estimated, and the quanti tative discrepancy between the two sets of results is explained with the di minished accuracy of the saddle-point approximation, implicit in the mean-f ield method, in the case of strongly fluctuating fields. (C) 2000 American Institute of Physics. [S0021-9606(00)51542-6].