Suppose we want to calculate the exact partition function Z
numerically. Need to do this for all T, but let's start with just
one temperature. For a real system, want O(
) spins, but let's
start small and try to solve for a 
lattice,
i.e. O(
) spins.
Number of configurations in the sum = 
.
Suppose we had a gigantic parallel supercomputer, with 10 million
processors. Each processor could generate a configuration C, calculate
and the Boltzmann factor 
and add it to the sum over configurations
in one nanosecond (less than the time for a single instruction for the
fastest modern computer).
We run this calculation for the age of the universe. This gives
procs 
configs/proc/sec
sec/yr 
yrs
configs (not real close to what is needed)