Path integral of spin models

Abstract

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.