Non-trivial Fixed Point of a ψ d 4 Fermionic Theory, II: Anomalous Exponent and Scaling Operators

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Statistical Mechanics

Background:

• Renormalization Group (RG) fixed-point theory is crucial for understanding critical phenomena.
• Fermionic models with quartic interactions and fractional kinetic terms present theoretical challenges.
• Previous work established constructive RG methods for similar systems.

Purpose of the Study:

• To investigate the RG fixed-point theory of a specific fermionic model in d=1,2,3 dimensions.
• To analyze the scaling properties of response functions and construct scaling operators.
• To determine the nature of critical exponents associated with these functions.

Main Methods:

• Utilizing a Grassmann functional integral formulation for the fermionic model.
• Applying constructive Renormalization Group methods with a fixed ultraviolet cutoff.
• Employing a convergent tree expansion for the generating function of correlations.

Main Results:

• Defined and constructed field and density scale-invariant response functions.
• Proved that the field response exponent is naive, while the density response exponent is anomalous and analytic.
• Constructed (almost-)scaling operators with specific correlation decay properties.

Conclusions:

• The study successfully applies constructive RG methods to a complex fermionic model.
• Anomalous scaling behavior is identified in density response functions, differing from naive predictions.
• The findings contribute to the understanding of critical phenomena in systems with relevant quartic interactions.