An additional characteristic of a magnet is a function of the ratio of internal fields

Authors
  • Semkin S.V.

    Sergey V. Semkin. Vladivostok State University of Economics and Service. Vladivostok. Russia

  • Smagin V.P.

    Viktor P. Smagin. Vladivostok State University of Economics and Service. Vladivostok. Russia

Abstract

In the theory of systems of interacting particles, the Ising model is often used. This model can serve as a fairly accurate description of real systems. In addition, the universality principle makes it possible to extend many of the results obtained for simple lattice Ising models to more complex systems. However, there are practically no exact solutions for the Ising model. In fact, the only exact solution is the Onsager solution for a square lattice. There are, of course, approximate methods of solution, but they have fundamental drawbacks, namely: approximate methods give overestimated estimates of the Curie temperature and incorrectly describe the behavior of the system near the phase transition point. However, as shown in this paper, there are ways to improve virtually any approximate methods. Using averaging over exchange fields, one can construct additional characteristics of magnetic systems, both near the phase transition point and beyond it. As such an additional characteristic, you can use the relation function. This function is defined as the ratio of such values of the
exchange interaction fields at which the cluster average of the spin is equal to the average over the ensemble. The paper considers the ratio function for clusters of one and two magnetic atoms. For the Ising model on a square lattice, the exact value of the ratio function is constructed using the Onsager
solution. For the same lattice, approximate values of the ratio function are constructed and compared with each other and with the exact value. The use of the ratio function makes it possible to construct new approximate solutions for the Ising model, making certain assumptions about this function.
Keywords: phase transitions, Ising model, сritical exponents.

Files
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