Why Might the Standard Large N Analysis Fail in the O(N) Model: The Role of Cusps in Fixed Point Potentials

Area of Science:

• Quantum Field Theory
• Statistical Mechanics
• Renormalization Group Theory

Background:

• The large N expansion is crucial for quantum and statistical field theory.
• Standard implementations may not capture all critical phenomena in field theories.

Purpose of the Study:

• To identify fixed points missed by the standard large N expansion in the O(N) model.
• To investigate the impact of these fixed points on multicritical physics at finite N.

Main Methods:

• Analysis of the O(N) model using the large N expansion.
• Investigation of renormalization group fixed points in dimensions less than four.
• Examination of effective potentials and boundary layer phenomena.

Main Results:

• The standard large N expansion misses certain renormalization group fixed points in dimensions < 4.
• These missed fixed points exhibit cusp singularities at N=∞, transitioning to boundary layers at finite N.
• The identified fixed points significantly influence the multicritical physics of the O(N) model at finite N.

Conclusions:

• The standard large N expansion is incomplete for describing all fixed points in certain field theories.
• The newly discovered fixed points and their associated phenomena are physically relevant for O(N) models.
• The mechanism is likely generic, also applying to models like O(N)⊗O(2).