  Fokker-Planck equations have been applied in the past to field theory topics
such as the stochastic quantization and the stabilization of bottomless action
theories. In this paper we give another application of the FP-techniques in a
way appropriate to the study of the ground state, the excited states and the
critical behaviour of quantum lattice Hamiltonians. With this purpose, we start
by considering a discrete or lattice version of the standard FP-Hamiltonian.
The well known exponential ansatz for the ground state wave functional becomes
in our case an exponential ``cluster" expansion. With a convenient choice for
this latter, we are able to construct FP-Hamiltonians which to a large extent
reproduce critical properties of ``realistic" quantum lattice Hamiltonians, as
the one of the Ising model in a transverse field (ITF). In one dimension, this
statement is made manifest by proving that the FP-Hamiltonian we built up
belongs to the same universality class as the standard ITF model or,
equivalently, the 2D-classical Ising model. To this respect, some
considerations concerning higher dimensional ITF models are outlined.
