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Ordered phase of the O(N) model within the nonperturbative renormalization group
Marcela Peláez1, Nicolás Wschebor1
1Instituto de Física, Facultad de Ingeniería, Universidad de la República, J.H.y Reissig 565, 11000 Montevideo, Uruguay.
Physical Review. E
|November 15, 2016
Summary
We analyzed nonperturbative renormalization group flow equations for scalar models, finding that regulator choice impacts flow smoothness. An improved numerical algorithm enhances stability for N>1, offering more reliable results.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
- Statistical Mechanics
Background:
- Nonperturbative renormalization group (RG) methods are crucial for understanding complex quantum field theories.
- Scalar models, like Z_{2} and O(N) invariant models, serve as fundamental testbeds for theoretical frameworks.
- The derivative expansion is a common approximation scheme in RG studies.
Purpose of the Study:
- To investigate nonperturbative renormalization group flow equations in the ordered phase of Z_{2} and O(N) scalar models.
- To analyze the impact of different regulators on flow properties within the local potential approximation (LPA).
- To develop and implement a more stable numerical algorithm for solving RG flow equations.
Main Methods:
- Analysis of nonperturbative renormalization group flow equations.
- Application of the derivative expansion scheme, focusing on the local potential approximation (LPA).
- Generalization of exact solutions for smooth flows and implementation of an improved numerical algorithm.
Main Results:
- Demonstrated that not all regulators yield smooth flows with convex free energy in the LPA.
- Identified regulators that lead to singular flows.
- Developed a generalized exact solution for smooth flows and implemented a numerically stable algorithm for N>1.
- Examined the impact of second-order derivative expansion on LPA results and field renormalization factors.
Conclusions:
- Regulator choice is critical for the validity of RG flows in scalar models.
- The developed numerical algorithm offers improved stability and accuracy for studying these models.
- Second-order derivative expansion refines understanding of flow behavior and renormalization factors.
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