Surprises in O(N) Models: Nonperturbative Fixed Points, Large N Limits, and Multicriticality

Area of Science:

• Theoretical Physics
• Condensed Matter Physics
• Quantum Field Theory

Background:

• The understanding of multicritical fixed points in O(N) models is crucial for various areas of physics.
• Previous studies suggested a simpler fixed point structure than what is observed.

Purpose of the Study:

• To investigate the detailed structure of multicritical fixed points in O(N) models.
• To explore the behavior of these fixed points in three dimensions (d=3) and in the large N limit (N=∞).
• To examine the relevance of these findings to O(N)⊗O(2) models in frustrated magnetic systems.

Main Methods:

• Nonperturbative analysis of O(N) models.
• Investigation of fixed point structures as functions of dimensionality (d) and the number of components (N).

Main Results:

• The multicritical fixed point structure of O(N) models is significantly more complex than previously assumed.
• New nonperturbative fixed points were identified in d=3 and at N=∞.
• An intricate double-valued structure of fixed points was revealed when viewed as functions of d and N.

Conclusions:

• The complexity of fixed points in O(N) models necessitates a revised theoretical framework.
• The identified fixed points and their double-valued nature offer new insights into critical phenomena.
• Shared features between O(N) and O(N)⊗O(2) models highlight their interconnectedness in describing complex magnetic systems.