Thermal Field Theory and the Finite-Temperature Renormalization Group

真人 坂本, 公一 船久保

István Gábor Márián, Andrea Trombettoni, I. Nándori

In this paper we discuss and revisit the finite temperature extension of the renormalization group (RG) treatment of T = 0 field theories, focusing as a case study on the ϕ 4 model. We first discuss the extension of RG equations of the very same model from T = 0 to finite T in the usual way by resorting to sums on the Matsubara frequencies and fixing the physical temperature parameter T . We show that this approach, although useful for a variety of applications, may lead to the disappearance of the critical points as extracted from the RG flow. Since the identification of fixed points is key in the study of classical and quantum phase transitions, we propose a modification of the usual finite-temperature RG approach by relating the temperature parameter to the running RG scale, T ≡ k T = τ k , where k T is the running cutoff for thermal and k is for the quantum fluctuations. Once this dimensionless temperature τ is introduced, we investigate the consequences on the thermal RG approach for the ϕ 4 model and construct its phase diagram. Finally, we formulate requirements for the phase diagram of the ϕ 4 theory based on known properties of the quantum and classical phase diagrams of the Ising model.

B. BHATTACHARYA

We have studied here the critical behaviors in a simple model from the point of view of the renormalization group at finite temperature utilizing the Stochastic field theoretic approach towards a finite temperature field theory. To this end, thermofield dynamics has been formulated in terms of Stochastic fields in the external and internal space and the thermal average of the two-point correlation function of the internal field functions is related with the order parameter. The thermodynamical functions and the critical phenomena are then studied constructing the generating functionals involving Stochastic fields.

Johannes Manus

Pierre Gosselin, B. Grosdidier, Hervé Mohrbach

Giorgio Frangi, Sašo Grozdanov

We study perturbative Wilsonian renormalization group (RG) for the scalar ϕ 4 theory at finite temperature to one loop order in the Schwinger-Keldysh closed-time-path (CTP) formalism. By explicitly integrating out the UV modes, we show how effective interactions coupling the two branches of the CTP contour arise. This provides a microscopic derivation of the type of effective CTP actions used in the literature. While the full effective theory has no critical points, we instead proceed to study critical properties of the RG flow in a reduced space of complex couplings that characterize certain time-ordered correlators and show the existence of two novel fixed points in d = 4 spacetime dimensions. We relate one to the Wilson-Fisher fixed point known to exist only in 4 − ε dimensions, and the other to the standard Gaussian fixed point.