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arXiv · 2508.16343

Quantifying time in Monte Carlo simulations: application to relaxation processes and AC susceptibilities of magnetic nanoparticles assemblies

A. Morjane·J. -G. Malherbe·J. -J. Alonso·F. Vernay·V. Russier
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Abstract

The study of the response of magnetic nanoparticles (MNP) assemblies to an external alternating magnetic field is of great interest for applications such as hyperthermia. The key quantity here is the complex susceptibility and its behavior in terms of temperature and frequency. From a theoretical point of view it can be obtained by Monte Carlo (MC) simulation with the time quantified Monte Carlo (TQMC) method if a physical time is associated with the MC step. Here we revisit this method by showing that the time unit can be derived from the MC stochastic process of the isolated particle. We first obtain a MC unit of time from the relaxation of the system at fixed temperature. Then this unit of time is used to compute complex susceptibilities. We show that it is now possible to match the TQMC results with actual experimental results regarding frequency dependent in phase susceptibilities and quantify the unit of time in seconds. Finally we show that the time unit obtained for the isolated particle remains valid when considering interacting particles such as the Heisenberg coupling or dipole dipole interactions.

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A. Morjane, J. -G. Malherbe, J. -J. Alonso, F. Vernay, V. Russier. 2025-08-22. Quantifying time in Monte Carlo simulations: application to relaxation processes and AC susceptibilities of magnetic nanoparticles assemblies. https://doi.org/10.1016/j.jmmm.2025.173443

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