Calculating field theories beyond the mean-field level

Mean-field theories are widely used as comparative theoretical tools throughout all areas of natural and engineering sciences. They are capable in many instances to deliver useful insights in properties and behavior of multi-body systems at relatively moderate computational costs. However, there are a multitude of cases were the mean-field approach has been found to provide either inaccurate or even qualitatively wrong results. In this article we present a new low-cost approach based on the method of Gaussian equivalent representation of Efimov and Ganbold, and show that it provides a far more accurate 0th-order approximation of the free energy and related thermodynamic and structural quantities than the mean-field approach. We demonstrate its effectiveness on the example of a polymer solution model in the dilute and semi-dilute regime.