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Related Experiment Video

Updated: Apr 19, 2026

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

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

A Eichhorn¹, D Mesterházy², M M Scherer³

¹Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, N2L 2Y5 Ontario, Canada.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 11, 2014

Summary

This study explores three coupled vector fields with O(N1)⊕O(N2)⊕O(N3) symmetry. Researchers found various interacting fixed points, including a novel symmetry-enhanced isotropic fixed point, with implications for understanding complex field theories.

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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.