Now K in this expression describes the coupling constant

to describe the interactions between neighboring adsorbed molecules.

An F bind is the free energy associated with binding of the absorbed molecule.

Now in this system, we need to take into account

the changes in the particular number of absorbed molecules.

Now what do you think?

Which ensemble should we pick?

Now the most convenient ensemble to pick is the grand canonical ensemble.

The grind canonical quotation function can be written in a standard way.

Now rather than carrying out a more detailed analysis of this equation

we will take a simpler approach and cast this in the language of the Eisen model.

What we need to do to do this Well, we need a change of variables where we can

relate the occupancy number NI to the spin variable SI by a linear transformation.

Now the simple mapping, maps the occupancy variable to a spin value of one.

When occupied, and a spin value of minus one when not occupied.

Now, this variable transformation allows us to recast the problem exactly

in the Eisen model.

In this expression, Z stands for

the coordination number of the lattice given by the number of nearest neighbors.

Now we have to remember to not double count, so

we need to divide this number by a factor of two.

So, for a two dimensional square lattice, the Z value takes two.

Therefore, with this exact map mapping of the current problem to the Ising model.

We can now evaluate all of these things in an analogous way to what we found in

the Ising model.

Therefore, we can exactly map our current problem

onto the Ising model with a suitable set of parameters.

The following parameter mapping holds for

the absorption case to the standardizing model.

Owing to the exact mapping between our current and the icing model,

we can note a few identical physical phenomena that arises in both systems.

Adsorption with interactions, exhibit of phase transition.