ABSTRACT
Mean field theory works well when R/a is large or the co-ordination number is large. In both cases, each degree of freedom is coupled to many neighbors. Mean field theory is exact when each spin is coupled to all other spins. In some complex situations, a systematic and relatively easy way to generate mean field theory is by extending the Hamiltonian to be infinite range. Another way of generating mean field theory is to allow the order parameter to have n components and to consider the case n → ∞. The chapter examines the limitations of the phenomenological theory. It provides the analysis which has been for the Landau theory of the Ising universality class. The chapter discusses the Gaussian approximation to the functional integral, and shows how the critical exponents are calculated the lowest order systematic correction to mean field theory.
