How does one go about solving the Ising model?
Want to work out thermodynamic averages of physically measurable quantities such as the magnetization M and the energy E as a function of the temperature T. The thermal average of M is
where 
is the magnetization of the configuration C, 
is the
probability distribution for the configuration as a function of T, and
the sum is over all configurations.
A fundamental result in statistical mechanics, which we will not derive here, but accept as a physical law, is that p is the Boltzmann distribution.