FD Statistics: The fermions have only two states, or 1. Thus, the grand canonical partition function for N indistinguishable fermions is given by

The number of particles is given by

Thus the average number of molecules in the s level is

This is the Fermi-Dirac (FD) distribution.

However, in the classical limit and BE and FD statistics lead to the classical MB statistics.

Fig. 1.2. plot of mean occupation number of a single-particle energy state ε in a system of non-interacting particles: curve 1 is for fermions, curve 2 for bosons and curve 3 for the particles obeying Maxwell-Boltzmann statistics.

In the discussion of critical phenomena in the coming chapters we will mostly consider either fluid system or localized spins. Both of them are well described by classical distinguishable particles and thus will follow MB statistics.