On the Theory of Randomly Dilute Ising and Heisenberg Ferromagnetics

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.