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Abstract

The finite-temperature properties of many magnetic materials are to a large degree influenced by spin fluctuations. The numerical simulation of these effects, however, faces several obstacles. In particular, the modelling of the magnetic interactions at the quantum-mechanical level should be neither oversimplified nor too computationally expensive. Furthermore, an efficient numerical sampler is required in order to treat the high-dimensional integration problem of the thermal expectation values. Our modelling approach are analytic bond-order potentials based on tight-binding. To treat the sampling problem, we extended the hybrid Monte Carlo sampler so that it will also work for the classical spin system. We furthermore developed an auxiliary-Hamiltonian method in order to improve the sampling efficiency. With this methodology, we simulate the magnetic phase transitions in BCC iron and determine the magnetic free energy difference between the BCC and FCC states of iron.