The Non-Interacting Magnetization Formula from the Pendulum Motion of Dipoles

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. On the second part of this paper the Maxwell-Boltzmann distribution is taken into account to determine the probability density function of the angular velocity. The ratio of the particles which has zero angular velocity in 2D is the maximum, in 3D is zero. Therefore the theoretical prediction is in better agreement with the exact formula of magnetization in 2D than in 3D. In this approach the effect of negative magnetization is able to come into existence in the non-interacting fluidum