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Non-interacting magnetization Taylor expansions are calculated in 2D and 3D at high external field according to the vibrational model. In this approach all dipoles are moved as a linear pendulum independent from each other. The temperature is taken into account according to the equipartition theorem, thus all particles have the same kinetic energy: kBT/2 in 2D and kBT in 3D. The expansions valid only at high external magnetic field due to the linearisation of initial differential equation. Ondoi:10.14232/analecta.2015.1.63-68 fatcat:unf6ppuffze7bhmhykiuiuqzrm