Abstract
Short-time propagator algorithms and a discrete-time formalism are used in combination with a basis set involving Grassmann variables coherent states to get the generating function associated to a system containing spin degrees of freedom. This generating function 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. The partition function, obtained as a cluster expansion expressed as an ordered sum over all possible sites, is more realistic than the partition function of the traditional Ising model involving only first neighbor interactions.
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