The Ising model has exact solutions in 1D and 2D. These do not
give the same results as mean-field theory for the critical exponents
and this observation opened
the way for the modern study of phase transitions.

In 3D there are only numerical approaches such as
simulations and series expansions. I will not discuss
the algorithms of these here (thats for the Computational Physics course)
but I will show some important features.
Both give the same numbers up to many figures of precision
so I guess we are getting it right.

finite field -
Sasha Gemintern
adapted this program for a finite field and canonical ensemble.

These both run on any linux machine or on tx, see also a local download link for the Creutz routines. The compile command is:
cc -O -o xising -L/usr/X11R6/lib xising.c -lm -lX11

Beautiful simulations in 3D - Lior Metzger did an undergraduate project
of visualizations of Ising models. This is also not difficult to run, but
for now I will just show some pictures.