Some Examples for the Lattice Gas

We consider the model of section 4.2.2. Each unit can be in one of two states, which we refer to as a hole h for an empty unit or w for an occupied state. In this model, the 2x2 matrix is 

Note the symmetrical roles of h and vi in these two limits. We shall see below that this symmetry is more general. 

For the nearest-neighbor pair distribution functions we have the following three 

In particular, the limit of the w—w pair correlation function should be noted. Although the probability distribution (4.3.96) is zero in this limit, the correlation between the two particles is finite. We have seen a similar situation in sections 3.2 and 3.3 and we shall see the analogue of (4.3.99) for liquids in Chapter 5. 

Although we shall not introduce the force between the particles—in this model the sites are fixed—it is useful to define the potential of average force by 

---