Quantum Thermal Expectation Values from an Effective Atomistic Spin Dynamics Model Using Path Integrals

In previous work, we have developed a method to approximate quantum thermal expectation values of a spin system using a path integral approach in the framework of atomistic spin dynamics. In the present work, we extend this model from a single spin coupled to a constant magnetic field, to the more general case of a system of spins coupled by isotropic Heisenberg interaction, in a potentially time-dependent magnetic field. In a first approximation, the classical atomistic model is extended by an effective field which for every interaction pair, depends only on the two interacting spins. This implies that we have a straightforward generalisation from 2 to N interacting spins. We compare our results to exactly solvable cases using exact diagonalisation for two-spins.