Numerical atom-to atom simulation of magnets, Bloch's 3/2 law and the third law of thermodynamics

The traditional model of a magnet «atom-to-atom» considers the magnetic moments of individual atoms connected by an exchange interaction. The evolution of magnetic moments is described on the basis of the Landau-Lifshitz equation, in which a random Langevin source is introduced, determined by the final temperature of the system. In this case, one of the main problems is the violation of the Bloch 3/2 law and the third law of thermodynamics. The recalculation of the intensity of a random source, carried out by Wuu et al., taking into account magnons provides the correct 5/2 asymptotics for the energy, but does not give the correct asymptotics for the magnetization. To solve this problem, we add a random delta-correlated in time but correlated in space source to the Langevin source. This approach, in conjunction with the Wuu approach, ensures the fulfillment of the third law of thermodynamics and Bloch's 3/2 law.