A Path Integral method for numerical simulations of Spin Dynamics

Following the way paved by path integral molecular dynamics, we build a classical spin model from which we can compute expectation values of a spin whilst taking into account its underlying quantisation, in the presence of a magnetic field. We express the spin algebra in terms of coherent spin states, which enable the transition from a discrete quantum system to an equivalent continuous classical model, and recast the quantum mechanics in the framework of path integrals. We approximate the path integral in the high-temperature limit and derive an effective classical Hamiltonian. The quantized nature of the spin manifests itself as an anisotropic effective field. Solving the effective classical model using atomistic spin dynamics, we calculate thermodynamic observables and show that our effective classical model produces accurate quantum expectation values within its relevant temperature range.