Second-order phase transitions in three dimensions

Abstract

The basic problem in the understanding of second-order phase transitions in three dimensions—based on the Landau Hamiltonian ℋ=1/2 (∇φ)2+1/2m2φ2 + (λ4/4!)φ4+…—is the appearance of strong infrared singularities which atT=Tc,i.e. m=0, explicitly do not allow an expansion in the coupling constantλ4. Therefore, in order to tame these strong infra-red divergences, one needs ana priori nonperturbative mechanism inλ4. We have presented such a nonperturbative solution, called screening, because of its analogy with what happens in the nonrelativistic electron gas. After screening, the theory gets the structure of a renormalizable field theory and one can then, using standard methods, obtain the full infra-red behaviour of the correlation functions, which give then immediately the critical exponents. In this paper, many aspects of this approach are reconsidered with extensive argumentation.