# Closed-form irreducible differential formulations of the Wilson renormalization group

## Abstract

We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon/sup 2/ the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon/sup 2/ by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator.

- Authors:

- Publication Date:

- Research Org.:
- Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

- OSTI Identifier:
- 5954596

- DOE Contract Number:
- AC02-76ER03069

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. A; (United States)

- Additional Journal Information:
- Journal Volume: 27:6

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; RENORMALIZATION; IRREDUCIBLE REPRESENTATIONS; EQUATIONS OF STATE; GINZBURG-LANDAU THEORY; PHASE TRANSFORMATIONS; RECURSION RELATIONS; SCALING LAWS; EQUATIONS; 657006* - Theoretical Physics- Statistical Physics & Thermodynamics- (-1987); 658000 - Mathematical Physics- (-1987)

### Citation Formats

```
Vvedensky, D D, Chang, T S, and Nicoll, J F.
```*Closed-form irreducible differential formulations of the Wilson renormalization group*. United States: N. p., 1983.
Web. doi:10.1103/PhysRevA.27.3311.

```
Vvedensky, D D, Chang, T S, & Nicoll, J F.
```*Closed-form irreducible differential formulations of the Wilson renormalization group*. United States. doi:10.1103/PhysRevA.27.3311.

```
Vvedensky, D D, Chang, T S, and Nicoll, J F. Wed .
"Closed-form irreducible differential formulations of the Wilson renormalization group". United States. doi:10.1103/PhysRevA.27.3311.
```

```
@article{osti_5954596,
```

title = {Closed-form irreducible differential formulations of the Wilson renormalization group},

author = {Vvedensky, D D and Chang, T S and Nicoll, J F},

abstractNote = {We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon/sup 2/ the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon/sup 2/ by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator.},

doi = {10.1103/PhysRevA.27.3311},

journal = {Phys. Rev. A; (United States)},

number = ,

volume = 27:6,

place = {United States},

year = {1983},

month = {6}

}

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