ABSTRACT
This chapter shows how two apparently different physical systems can be described by mean field theory. In the Van der Waals gas, each particle interacts with the average density due to all the other gas particles. In the Weiss model of ferromagnetism, each spin interacts with the average magnetic field due to the magnetisation of the other spins. The chapter addresses the question of why the critical exponents are the same for both the Van der Waals fluid and the Weiss ferromagnet. It considers some examples of order parameters, with differing numbers of components. Landau theory may be motivated by a systematic calculation from the microscopic Hamiltonian. One remark about cubic terms in Landau theory. The Landau criterion is only a statement made within the context of mean field theory. It is important to realize that the fluctuation effects omitted by mean field theory can change the order of a transition.
