I show that Ising models and $Z(2)$ gauge theories, in any number of dimensions, are equivalent to systems of fermions with local interactions only. This is done in the Hamiltonian formalism by rewriting the Hamiltonians in terms of locally coupled fermion operators. One advantage of the fermionic formalism is that duality transformations become trivial. All unsolved models have products of four or more fermion operators as terms in their Hamiltonians.I show that Ising models and $Z(2)$ gauge theories, in any number of dimensions, are equivalent to systems of fermions with local interactions only. This is done in the Hamiltonian formalism by rewriting the Hamiltonians in terms of locally coupled fermion operators. One advantage of the fermionic formalism is that duality transformations become trivial. All unsolved models have products of four or more fermion operators as terms in their Hamiltonians.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsMay 15, 198015 citations

I show that Ising models and

Z(2)

gauge theories, in any number of dimensions, are equivalent to systems of fermions with local interactions only. This is done in the Hamiltonian formalism by rewriting the Hamiltonians in terms of locally coupled fermion operators. One advantage of the fermionic formalism is that duality transformations become trivial. All unsolved models have products of four or more fermion operators as terms in their Hamiltonians.