Completeness of classical $\phi^4$ theory on 2D lattice

We formulated a quantum formalism for the statistical mechanical models of discretized field theories on lattices and then showed that the discrete version of $\phi^4$ theory on 2D square lattice is complete in the sense that the partition function of any other discretized scalar field theory on an arbitrary lattice with arbitrary interactions can be realized as a special case of the partition function of this model.