Path integral of spin models

A path-integral representation of 1D Ising and XY spin models is investigated. Short-time propagator algorithms and a discrete time formalism are used in combination with Grassmann variables non-orthogonal coherent states to get a many-body analytic propagator. Fermion operators satisfying the canonical anticommutation relations are constructed from the rising and lowering spin operators via the Jordan-Wigner transformation. Computation of the partition function and thermodynamic properties follows from an appropriate tracing over Grassmann variables in the imaginary time domain