On the Theory of Randomly Dilute Ising and Heisenberg Ferromagnetics

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Abstract
The Brout expansion for the free energy of the Ising or Heisenberg model is formally summed over all interaction graphs with not more than m vertices: the result is expressed in terms of the partition functions of isolated physical clusters, again having not more than m vertices. These partition functions are multiplied by occurrence factors closely related to the occurrence factors for the corresponding isolated physical clusters in a randomly dilute ferromagnet at low concentrations of the magnetic elements. Comparison is made with earlier work on the randomly dilute Ising and Heisenberg models.