Asymptotic behavior of the susceptibility and magnetization of a diluted Ising magnet

• 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

It is known that the properties of dilute and disordered magnets differ from the properties of pure magnets. However, exact solutions for models of magnetic systems with dilution have not yet been obtained. Therefore, it makes sense to construct approximate solutions for dilute magnets. Some of these solutions can be constructed by averaging over the interaction fields. The  application  of  the  distribution  function  over  interaction  fields  to  the  study  of  the properties of a  system of many interacting particles has been used for a  long time. In
previous works of the authors, the method of averaging over exchange fields was applied to the analysis of the magnetic properties of pure and diluted magnets. In this paper, we formulate and prove the relations on which the method of averaging over  exchange  fields  can  be  based  on  clusters  of  several  spins.  Application  of  the  obtained relations to the Ising model with bond dilution allowed us to construct two vari-
ants  of  approximate  methods  for  this  model  (as  an  example).  The  magnetization  obtained  in  these  approximations  at  zero  temperature  is  compared  with  the  probability that the site of a Bethe lattice diluted in bonds belongs to an infinite cluster.
In the same approximations, the magnetic susceptibility of a diluted Ising magnet was also found. In both approximations, in the region of the absence of spontaneous magnetization for susceptibility in a zero external field, the same result is obtained. In the region of spontaneous magnetization, the susceptibility in different approximations is different, but its asymptotic behavior is the same in both approximations.
Keywords: phase transitions, Ising model, diluted magnet.