An interacting spin system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short-time propagator algorithms and a discrete time formalism are used in combination with a basis set involving Grassmann variables coherent states to get a many-body analytic propagator. The generating function thus obtained leads, after an adequate tracing over Grassmann variables in the imaginary time domain, to the partition function. A spin 1/2 Hamiltonian involving the whole set of interactions is considered. Fermion operators satisfying the standard anticommutation relations are constructed from the raising and lowering spin operators via the Jordan-Wigner transformation. The partition function obtained is more general than the partition function of the traditional Ising model involving only first-neighbor interactions. Computations were performed assuming that the coupling as a function of the distance can be reasonably well represented by an Airy function.

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