Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark

Area of Science:

• Statistical Physics
• Quantum Field Theory

Background:

• Nonperturbative renormalization-group (RG) methods are crucial for studying complex systems out-of-equilibrium.
• Implementing regulators in RG flow equations is essential for obtaining reliable results.
• Existing regulators may not fully satisfy physical constraints like causality and the fluctuation-dissipation theorem.

Purpose of the Study:

• To derive conditions for implementing regulators dependent on both momentum and frequency in out-of-equilibrium RG flow equations.
• To investigate the necessity of frequency regulators for self-consistent application of the principle of minimal sensitivity (PMS).
• To compute the dynamical critical exponent (z) for model A as a benchmark.

Main Methods:

• Derivation of necessary conditions for momentum- and frequency-dependent regulators.
• Application of nonperturbative renormalization-group flow equations.
• Computation of the dynamical critical exponent (z) for model A.
• Analysis of regulator compatibility with causality and the fluctuation-dissipation theorem.
• Optimization of critical exponents (η, ν, z) using the principle of minimal sensitivity (PMS).

Main Results:

• Established the necessary conditions for implementing combined momentum and frequency regulators.
• Demonstrated that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be constructed.
• Computed the dynamical critical exponent (z) for model A.
• Showed that frequency regulators are indispensable for the self-consistency of the PMS criterion when optimizing critical exponents.

Conclusions:

• Frequency and momentum regulators are crucial for advanced nonperturbative renormalization-group studies.
• The developed regulators ensure physical consistency and enable self-consistent optimization of critical exponents.
• This work provides a framework for more accurate theoretical predictions in out-of-equilibrium statistical systems.