Scaling relations and multicritical phenomena from Functional Renormalization

Abstract

We investigate multicritical phenomena in O(N)+O(M)-models by means of nonperturbative renormalization group equations. This constitutes an elementary building block for the study of competing orders in a variety of physical systems. To identify possible multicritical points in phase diagrams with two ordered phases, we compute the stability of isotropic and decoupled fixed point solutions from scaling potentials of single-field models. We verify the validity of Aharony's scaling relation within the scale-dependent derivative expansion of the effective average action. We discuss implications for the analysis of multicritical phenomena with truncated flow equations. These findings are an important step towards studies of competing orders and multicritical quantum phase transitions within the framework of Functional Renormalization.

10 pages, published version

References in corpus (8)

• Interactions and phase transitions on graphene's honeycomb lattice
• The critical exponents of the superfluid transition in He4
• Renormalization Group Approach towards the QCD Phase Diagram
• Ultracold atoms and the Functional Renormalization Group
• Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition
• Scaling Solutions in Continuous Dimension
• Field theory of bi- and tetracritical points: Statics
• Stability of fixed points and generalized critical behavior in multifield models