Approximations to Brillouin functions for analytic descriptions of ferromagnetism

The statistical theory of magnetism leads to the magnetic field appearing in the two terms of the Brillouin function, both of which are transcendental, making it impossible to solve explicitly for the argument of that function. The replacement of the Brillouin function B(J)(x) by a square root function yields simple algebraic expressions for mean field treatments of cooperative magnetic phenomena. This is useful in the teaching of ferromagnetism. (C) 2008 American Institute of Physics.