Thermodynamic functions and frustration properties of magnets

• Semkin S.V.

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

• Smagin V.P.

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

In the present work, expressions are obtained that make it possible to calculate the free energy and entropy for a magnetic system, for which there is an exact or approximate expression for the magnetization. The derivation of these expressions is based only on the
asymptotic behavior of the magnetization with an increase in the external field and on the value of the Hamiltonian of the magnetic system in the saturation state. Therefore, the result obtained can easily be extended to a fairly wide class of magnetic models, both pure
and with nonmagnetic dilution. The obtained expression for the magnetic entropy can serve as a means of analyzing the frustrated state in the system. As a sign of frustration of the magnetic system, the work uses the difference from zero of the entropy of the ground
state. The one-dimensional Ising model in an external field with the interaction of only the nearest neighbors is used as an example of a magnetic system that allows the occurrence of frustrations. Analysis of the expression for the magnetization of this model makes it possible
to construct a phase diagram of the ground state. The phase variables in this diagram are the constant of the exchange interaction of the nearest neighbors and the magnitude of the external field. The diagram consists of three two-dimensional regions with positive,
negative and zero magnetization, respectively. The boundaries between these areas can be considered as separate areas of the diagram with their own values of magnetization. Analysis of the expression for the entropy shows that the entropy of the ground state vanishes
at the interior points of the areas of the diagram, which indicates the absence of frustrations in these areas. The entropy of the ground state is nonzero at the boundaries of regions with zero and nonzero magnetization.
Keywords: phase transitions, frustration, Ising model, phase diagram.