  The exact factorized ground state of a heterogeneous (ferrimagnetic) spin
model which is composed of two spins ($\rho, \sigma$) has been presented in
detail. The Hamiltonian is not necessarily translational invariant and the
exchange couplings can be competing antiferromagnetic and ferromagnetic
arbitrarily between different sub-lattices to build many practical models such
as dimerized and tetramerized materials and ladder compounds. The condition to
get a factorized ground state is investigated for non-frustrated spin models in
the presence of a uniform and a staggered magnetic field. According to the
lattice model structure we have categorized the spin models in two different
classes and obtained their factorization conditions. The first class contains
models in which their lattice structures do not provide a single uniform
magnetic field to suppress the quantum correlations. Some of these models may
have a factorized ground state in the presence of a uniform and a staggered
magnetic field. However, in the second class there are several spin models in
which their ground state could be factorized whether a staggered field is
applied to the system or not. For the latter case, in the absence of a
staggered field the factorizing uniform field is unique. However, the degrees
of freedom for obtaining the factorization conditions are increased by adding a
staggered magnetic field.
