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We show how quasiprobability distribution functions defined over$N^{2}$-dimensional discrete phase spaces can be used to treat physical systemsdescribed by a finite space of states which exhibit spin tunneling effects.This particular approach is then applied to the Lipkin-Meshkov-Glick model inorder to obtain the time evolution of the discrete Husimi function, and as aby-product the energy gap for a symmetric combination of ground and firstexcited states. Moreover, we also show how an angle-based potential approachcan be efficiently employed to explain qualitatively certain features of theenergy gap in terms of a spin tunneling. Entropy functionals are also discussedin this context. Such results reinforce not only the formalism per se but alsothe possibility of some future potential applications in other branches ofphysics.

Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model