  We show that the partition function of all classical spin models, including
all discrete Standard Statistical Models and all abelian discrete Lattice Gauge
Theories (LGTs), can be expressed as a special instance of the partition
function of the 4D Z_2 LGT. In this way, all classical spin models with
apparently very different features are unified in a single complete model, and
a physical relation between all models is established. As applications of this
result, we present a new method to do mean field theory for abelian discrete
LGTs with d>3, and we show that the computation of the partition function of
the 4D Z_2 LGT is a computationally hard (#P-hard) problem. We also extend our
results to abelian continuous models, where we show the approximate
completeness of the 4D Z_2 LGT. All results are proven using quantum
information techniques.
