Multi-group approximation

One of the methods for an approximate description and study of a system of a large number of interacting particles (gas, fluid), used in statistical physics.

The method is based on the assumption that every (or almost-every) configuration of particles can be divided into finite groups of particles, clusters, situated sufficiently far apart and almost not interacting with each other. In other words, the system of interacting particles is assumed to be in the form of gas clusters which are not allowed to come too close together. The next step lies in neglecting these restrictions, and also in excluding from the discussion clusters of very large size or of very complicated form (this properly constitutes the multi-group approximation).

The basic assumption that a configuration decomposes into clusters, which underlies this method, is true for low particle density and for short-range forces between them. Whether this assumption holds in other cases is unknown (1989). The method of multi-group approximation, apparently, gives a good approximation only for low densities and becomes too coarse in the case of a phase transition, when clusters of all sizes begin to play a comparably important role.

References

[1]	W. Band, J. Chem. Phys. , 7 (1939) pp. 324–326
[2]	J. Frenkel, J. Chem. Phys. , 7 (1939) pp. 200
[3]	R.A. Minlos, Ya.G. Sinai, "The phenomenon of "phase separation" at low temperatures in some lattice models of a gas I" Math. USSR Sb. , 2 : 3 (1967) pp. 335–395 Mat. Sb. , 73 : 3 (1967) pp. 375–448
[4]	T.L. Hill, "Statistical mechanics" , McGraw-Hill (1956)