  We propose an approach which allows to construct and use a potential function
written in terms of an angle variable to describe interacting spin systems. We
show how this can be implemented in the Lipkin-Meshkov-Glick, here considered a
paradigmatic spin model. It is shown how some features of the energy gap can be
interpreted in terms of a spin tunneling. A discrete Wigner function is
constructed for a symmetric combination of two states of the model and its time
evolution is obtained. The physical information extracted from that function
reinforces our description of phase oscillations in a potential.
