  Spin models are used in many studies of complex systems---be it condensed
matter physics, neural networks, or economics---as they exhibit rich
macroscopic behaviour despite their microscopic simplicity.
  Here we prove that all the physics of every classical spin model is
reproduced in the low-energy sector of certain `universal models'.
  This means that (i) the low energy spectrum of the universal model reproduces
the entire spectrum of the original model to any desired precision, (ii) the
corresponding spin configurations of the original model are also reproduced in
the universal model, (iii) the partition function is approximated to any
desired precision, and (iv) the overhead in terms of number of spins and
interactions is at most polynomial.
  This holds for classical models with discrete or continuous degrees of
freedom.
  We prove necessary and sufficient conditions for a spin model to be
universal, and show that one of the simplest and most widely studied spin
models, the 2D Ising model with fields, is universal.
