I am not sure how to look for references for the following problem. Imagine having a collection of 2 kinds of particles of density $n_1$ and $n_2$ that can arrange themselves in clusters (e.g., something like protons and neutrons that can arrange themselves in nuclei). For a given temperature and chemical composition (i.e., given values of $n_1$ and $n_2$ in a specified fixed volume) there should be a statistically well-defined fraction of particles that are not bound in any cluster and a distribution of clusters (possibly of different sizes and composition): which are the methods or approximations that have been developed to study this kind of systems? 

Starting from the Hamiltonian of the system (something like $K_1+K_2+V_{11}+V_{22}+V_{12}$, where $K_i$ is the kinetic term for the $i$-species and $V_{ij}$ is the 2-body potential between $i$-species and $j$-species particles, $i,j=1,2$), one could in principle calculate the configurational probability of a microstate (Gibbs weight) or the partition function. However, this "ab-initio" approach seems too general and difficult to be useful. **Is there any method or approximation that may be used to find the distribution of clusters?** Are there any criteria to assess if the system will be "homogeneous" (i.e. a gas/liquid of homogeneously mixed particles of the two species) or a collection of clusters?

**Note:** the [cluster expansion][1] is a cool and useful method but it's not directly related to the "clusters" I am considering here... or at least I see no direct connection. Somehow, I have the feeling that this kind of problem is more similar to the problem of ionization leading to the [Saha equation][2] (some electrons can be free and others in bound states).  


  [1]: https://Cluster%20expansion
  [2]: https://en.wikipedia.org/wiki/Saha_ionization_equation