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Nonperturbative renormalization group preserving full-momentum dependence: implementation and quantitative

F Benitez¹, J-P Blaizot, H Chaté

¹LPTMC, CNRS-UMR 7600, Université Pierre et Marie Curie, F-75252 Paris, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|April 3, 2012

Summary

This study implements the Blaizot-Méndez-Wschebor approximation for nonperturbative renormalization group calculations. The method accurately computes full-momentum dependence of correlation functions in scalar O(N) theories.

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Area of Science:

Theoretical Physics
Quantum Field Theory
Statistical Mechanics

Background:

The renormalization group (RG) is crucial for understanding systems near critical points.
Nonperturbative RG methods are essential for complex quantum field theories.
Existing schemes like the derivative expansion have limitations in capturing full momentum dependence.

Purpose of the Study:

To implement and detail the Blaizot-Méndez-Wschebor (BMW) approximation scheme for nonperturbative renormalization group calculations.
To enable the computation of the full-momentum dependence of correlation functions.
To assess the scheme's performance and compare it with other methods.

Main Methods:

Detailed implementation of the Blaizot-Méndez-Wschebor approximation scheme.
Application to scalar O(N) theories as a test case.
Calculation of critical exponents, the two-point function at criticality, and the universal structure factor.

Main Results:

The BMW scheme successfully computes the full-momentum dependence of correlation functions.
Quantitative results for scalar O(N) theories show very good agreement with existing high-precision results.
Accurate predictions for critical exponents, the two-point function, and the structure factor were obtained.

Conclusions:

The Blaizot-Méndez-Wschebor approximation scheme is a powerful tool for nonperturbative quantum field theory calculations.
The scheme provides accurate results across different momentum regimes and phases.
It offers a significant advancement over methods limited to specific momentum scales, like the derivative expansion.