We investigate the spin and field systems on a lattice connected by the Kac-Siegert transform. It is shown that the structures of corresponding theories are equivalent (in the sense of isomorphy of space of Gibbs states and order parameters). Using the idea of equivalence of spin and field pictures, we exhibit a class of lattice systems possessing infinitely uncountably many ground states. The systems of this type with infinite-range, slow-decaying interactions are expected to have a spin-glass phase transition.