# Nonuniversal quantities from dual renormalization group transformations

## Abstract

Using a simplified version of the renormalization group (RG) transformation of Dyson[close quote]s hierarchical model, we show that one can calculate all the nonuniversal quantities entering into the scaling laws by combining an expansion about the high-temperature fixed point with a dual expansion about the critical point. The magnetic susceptibility is expressed in terms of two dual quantities transforming covariantly under an RG transformation and has a smooth behavior in the high-temperature limit. Using the analogy with Hamiltonian mechanics, the simplified example discussed here is similar to the anharmonic oscillator, while more realistic examples can be thought of as coupled oscillators, allowing resonance phenomena. [copyright] [ital 1999] [ital The American Physical Society]

- Authors:

- (Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States))

- Publication Date:

- OSTI Identifier:
- 6272481

- Alternate Identifier(s):
- OSTI ID: 6272481

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

- Additional Journal Information:
- Journal Volume: 60:3; Journal ID: ISSN 1063-651X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANHARMONIC OSCILLATORS; LATTICE FIELD THEORY; MAGNETIC SUSCEPTIBILITY; RENORMALIZATION; SCALING LAWS; FIELD THEORIES; MAGNETIC PROPERTIES; PHYSICAL PROPERTIES; QUANTUM FIELD THEORY 662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)

### Citation Formats

```
Meurice, Y., and Niermann, S.
```*Nonuniversal quantities from dual renormalization group transformations*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevE.60.2612.

```
Meurice, Y., & Niermann, S.
```*Nonuniversal quantities from dual renormalization group transformations*. United States. doi:10.1103/PhysRevE.60.2612.

```
Meurice, Y., and Niermann, S. Wed .
"Nonuniversal quantities from dual renormalization group transformations". United States. doi:10.1103/PhysRevE.60.2612.
```

```
@article{osti_6272481,
```

title = {Nonuniversal quantities from dual renormalization group transformations},

author = {Meurice, Y. and Niermann, S.},

abstractNote = {Using a simplified version of the renormalization group (RG) transformation of Dyson[close quote]s hierarchical model, we show that one can calculate all the nonuniversal quantities entering into the scaling laws by combining an expansion about the high-temperature fixed point with a dual expansion about the critical point. The magnetic susceptibility is expressed in terms of two dual quantities transforming covariantly under an RG transformation and has a smooth behavior in the high-temperature limit. Using the analogy with Hamiltonian mechanics, the simplified example discussed here is similar to the anharmonic oscillator, while more realistic examples can be thought of as coupled oscillators, allowing resonance phenomena. [copyright] [ital 1999] [ital The American Physical Society]},

doi = {10.1103/PhysRevE.60.2612},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

issn = {1063-651X},

number = ,

volume = 60:3,

place = {United States},

year = {1999},

month = {9}

}