In the framework of the renormalization-group (RG) approach, critical
phenomena can be investigated by studying the RG flow of multi-parameter
Φ4 field theories with an N-component fundamental field, containing up
to 4th-order polynomials of the field. Some physically interesting systems
require Φ4 field theories with several quadratic and quartic parameters,
depending essentially on their symmetry and symmetry-breaking pattern at the
transition. Results for their RG flow apply to disorder and/or frustrated
systems, anisotropic magnetic systems, density wave models, competing orderings
giving rise to multicritical behaviors. The general properties of the RG flow
in multi-parameter Φ4 field theories are discussed. An overview of
field-theoretical results for some physically interesting cases is presented,
and compared with other theoretical approaches and experiments. Finally, this
RG approach is applied to investigate the nature of the finite-temperature
transition of QCD with Nf light quarks.Comment: 22 pages, Plenary talk at the XXV International Symposium on Lattice
Field Theory, July 30 - August 4 2007, Regensburg, German