Grupo de renormalização variacional: uma abordagem para o potencial efetivo à temperatura finita de uma teoria escalar

Abstract

This work investigates the issues of scale dependence present in thermal resummation approaches, such as those produced by the Optimized Perturbation Theory (OPT). To address this challenge, this work proposes a prescription that enhances the effective potential of OPT through a methodology called Renormalization Group Improvement (RGI). This approach modifies the effective potential of the theory by including new terms that ensure renormalization group invariance, thereby significantly reducing scale dependence without altering the standard procedures of OPT. The application of the RGI methodology in the context of OPT, leading to what we call Variational Renormalization Group (VRG), when applied to the finite temperature λϕ4 model, produced promising results in reducing the scale dependence in different thermodynamic quantities. In the symmetric phase, a notable reduction in scale dependence was observed for values of the coupling (λ > 1). In the broken phase, for large values of coupling and field, the VRG effectively mitigated the scale dependence while preserving the second-order phase transition universality class of the λϕ4 model. For small couplings, the results obtained by the VRG resemble those of the OPT, with a slight advantage observed for the OPT.