  We present general mappings between classical spin systems and quantum
physics. More precisely, we show how to express partition functions and
correlation functions of arbitrary classical spin models as inner products
between quantum stabilizer states and product states, thereby generalizing
mappings for some specific models established in [Phys. Rev. Lett. 98, 117207
(2007)]. For Ising- and Potts-type models with and without external magnetic
field, we show how the entanglement features of the corresponding stabilizer
states are related to the interaction pattern of the classical model, while the
choice of product states encodes the details of interaction. These mappings
establish a link between the fields of classical statistical mechanics and
quantum information theory, which we utilize to transfer techniques and methods
developed in one field to gain insight into the other. For example, we use
quantum information techniques to recover well known duality relations and
local symmetries of classical models in a simple way, and provide new classical
simulation methods to simulate certain types of classical spin models. We show
that in this way all inhomogeneous models of q-dimensional spins with pairwise
interaction pattern specified by a graph of bounded tree-width can be simulated
efficiently. Finally, we show relations between classical spin models and
measurement-based quantum computation.
