ABSTRACT
This chapter discusses a very popular method of studying critical phenomena analytically: the so-called ϵ-expansion. It describes the renormalisation group calculation of the critical exponents in the complete Landau theory, near d = 4. The chapter outlines the strategy of the calculation of <V>0, to prepare the reader for the algebraic horrors to follow. R. P. Feynman developed useful shorthand for the terms, which is to write down diagrams indicating how different fields are paired up. There is one-to-one correspondence between each Feynman diagram or Feynman graph and a term in the perturbation series. This correspondence is not unique: there are many ways to write down diagrams for the terms, and people have their own preferences. Once one has figured out this correspondence, then one only has to be able to draw all the appropriate diagrams to see what one should compute.
