Infra-red behaviour ofϕ 4 theory in three dimensions and connection with critical phenomenatheory in three dimensions and connection with critical phenomena

Abstract

Using a theory that establishes a proof of scaling—accepting the renormalization group methods of field theory, as formalized in the Callan-Symanzik equation—for the infra-red behaviour ofϕ4 field theory in all continuous numbers of dimensions below four, we present in this paper a discussion of the introduction of theN-dependence, whereN is the number of components of the field ϕ(x). These results describe also the scaling behaviour, based on the Landau Hamiltonian, of second-order phase transitions. The effect of the termϕ6(x), which also contributes to the infra-red behaviour in three dimensions, is briefly discussed.