Renormalization-group approach to critical behaviors in thermo field dynamics

We have studied critical behaviors in a simple model by means of a two-parameter Abelian renormalization group. The scaling law γ' = ν'(2-eta) is a natural result in our framework, while some plausible assumptions were needed to derive the other scaling laws α' + 2β + γ' = 2 and α' + β(delta + 1) = 2. In this paper we related the real-time Green's functions to thermodynamical quantities by means of the thermo field dynamics. This may serve as a preparation for our future study of the behavior of dynamical (i.e., time-dependent) quantities around critical points. (J.P.N.)