Stability of φ^{4}-vector model: Four-loop ε expansion study.

Area of Science:

• Quantum Field Theory
• Statistical Mechanics
• Renormalization Group Theory

Background:

• O(n)-symmetric φ⁴-field theory typically considers n=d components.
• A neglected term, proportional to the squared divergence of the field, can alter critical behavior.
• This term requires detailed study for new fixed points and their stability.

Purpose of the Study:

• To investigate the impact of the neglected term on critical phenomena in O(n)-symmetric models.
• To determine the stability of fixed points associated with this term.
• To calculate higher-order contributions to the stability exponent ωh.

Main Methods:

• Renormalization group analysis in d=4-2ɛ dimensions.
• Four-loop calculations within the minimal subtraction scheme.
• Perturbation theory to higher orders.

Main Results:

• The stability exponent ωh was calculated to four-loop order.
• The value of ωh was found to be positive: 0.0156(3).
• This positive value suggests the neglected term can be disregarded for critical behavior analysis.

Conclusions:

• The frequently neglected term in O(n)-symmetric φ⁴-field theory actions does not alter the fundamental nature of critical behavior.
• Despite being negligible for stability, the small positive value of ωh indicates significant corrections to critical scaling over a wide range.