A PROBABILITY DENSITY COMMON TO MOLECULAR FIELD AND COLLECTIVE EXCITATION THEORIES OF FERROMAGNETISM

Molecular field theory is frequently used to relate the higher moments <(S(z))(n)> to the first moment <S(z)>, the latter quantity being known from empirical magnetization data. The results are in excellent agreement with experiment, despite the glaring inadequacies of molecular field theory. It is shown that the functional dependence of <(S(z))(n) > on <S(z)> follows only from a particular feature of molecular field theory, which has much wider generality and validity. The same result is obtained in all quasi-independent collective excitation theories. This fact is corroborated in decoupled Green function theories, and is used to simplify the form of these latter theories.