  The Ising model is an equilibrium stochastic process used as a model in
several branches of science including magnetic materials, geophysics,
neuroscience, sociology and finance. Real systems of interest have finite size
and a fixed coupling matrix exhibiting quenched disorder. Exact methods for the
Ising model, however, employ infinite size limits, translational symmetries of
lattices and the Cayley tree, or annealed structures as ensembles of networks.
Here we show how the Ising partition function can be evaluated exactly by
exploiting small tree-width. This structural property is exhibited by a large
set of networks, both empirical and model generated.
