Correction of coarse-graining errors by a two-level method: Application to the Asakura-Oosawa model

We present a method that exploits self-consistent simulation of coarse-grained and fine-grained models in order to analyze properties of physical systems. The method uses the coarse-grained model to obtain a first estimate of the quantity of interest, before computing a correction by analyzing properties of the fine system. We illustrate the method by applying it to the Asakura-Oosawa model of colloid-polymer mixtures. We show that the liquid-vapor critical point in that system is affected by three-body interactions which are neglected in the corresponding coarse-grained model. We analyze the size of this effect and the nature of the three-body interactions. We also analyze the accuracy of the method as a function of the associated computational effort.