In this section the general form for the distribution of any subset of the system sites is developed. Consider any set of k distinct spins of the n spin system. Let
be the indices of these spins, and without loss of generality let 
. Label the spin values 
, and the rest of the spin values 
. With this notation, define the partition functions 
, where the number of spins is made explicit in the subscript, but their locations are only made explicit as arguments, as is typical in descriptions of many body distribution functions.
where we identify 
with 
. Simplifying 
we find immediately that
where 
is taken to be 
. Write the probability for the spin state 
directly as
where 
.