  We establish a connection between ground states of local quantum Hamiltonians
and thermal states of classical spin systems. For any discrete classical
statistical mechanical model in any spatial dimension, we find an associated
quantum state such that the reduced density operator behaves as the thermal
state of the classical system. We show that all these quantum states are unique
ground states of a universal 5-body local quantum Hamiltonian acting on a
(polynomially enlarged) system of qubits arranged on a 2D lattice. The only
free parameters of the quantum Hamiltonian are coupling strengthes of two-body
interactions, which allow one to choose the type and dimension of the classical
model as well as the interaction strength and temperature.
