  The partition function of the 2D Ising model coupled to an external magnetic
field is studied. We show that the sum over the spin variables can be reduced
to an integration over a finite number of variables. This integration must be
performed numerically. But in order to reduce the partition function we must
introduce as many different coupling constants as spin variables. The total
memory that we need in order to store these coupling constants imposed
important restrictions on the number of spin variables.
