Stability of fixed points and generalized critical behavior in multifield models.

Area of Science:

• Quantum Field Theory
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Understanding critical phenomena in systems with multiple interacting fields is crucial.
• Symmetries play a key role in determining the behavior of physical systems at critical points.
• Previous studies focused on two-field models, leaving three-field systems less explored.

Purpose of the Study:

• To investigate the phase structure of models with three coupled vector fields under O(N1)⊕O(N2)⊕O(N3) symmetry.
• To identify and characterize interacting fixed points and their stability properties.
• To compare the findings with related two-field models and multifield systems.

Main Methods:

• Utilizing the nonperturbative functional renormalization group (FRG) technique.
• Deriving beta functions for couplings and anomalous dimensions in d dimensions.
• Analyzing fixed points and their stability for all values of N1, N2, and N3.

Main Results:

• Discovery of a symmetry-enhanced isotropic fixed point generalizing the O(N) Wilson-Fisher fixed point.
• Identification of a large class of fixed points with partial symmetry enhancement.
• Characterization of partially and fully decoupled fixed-point solutions and their stability properties.
• Observation of no stable fixed points for small numbers of field components, attributed to complex coupling landscapes.

Conclusions:

• The study reveals a rich fixed-point structure in three-field models, distinct from two-field systems.
• Fixed-point collisions are identified as a mechanism for stability interchange.
• The findings provide insights into the behavior of complex quantum field theories and critical phenomena.