# Hyperscaling in the broken symmetry phase of Dyson's hierarchical model

## Abstract

We use polynomial truncations of the Fourier transform of the local measure to calculate the connected q-point functions of Dyson's hierarchical model in the broken symmetry phase. We show that accurate values of the connected one-, two-, and three-point functions can be obtained at large volume and in a limited range of constant external field coupled linearly to the field variable. We introduce a new method to obtain the correct infinite volume and zero external field extrapolations. We extract the leading critical exponents and show that they obey the scaling and hyperscaling relations with an accuracy ranging from 10{sup -5} to 5x10{sup -3}. We briefly discuss how to improve the method of calculation. (c) 2000 The American Physical Society.

- Authors:

- Department de Fisica, CINVESTAV-IPN , Ap. Post. 14-740, Mexico, D.F. 07000, (Mexico)
- Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States)

- Publication Date:

- OSTI Identifier:
- 20216473

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. D, Particles Fields

- Additional Journal Information:
- Journal Volume: 61; Journal Issue: 11; Other Information: PBD: 1 Jun 2000; Journal ID: ISSN 0556-2821

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM FIELD THEORY; SCALING LAWS; SYMMETRY BREAKING; EXTRAPOLATION; FOURIER TRANSFORMATION; POLYNOMIALS; THEORETICAL DATA

### Citation Formats

```
Godina, J. J., Meurice, Y., and Oktay, M. B.
```*Hyperscaling in the broken symmetry phase of Dyson's hierarchical model*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevD.61.114509.

```
Godina, J. J., Meurice, Y., & Oktay, M. B.
```*Hyperscaling in the broken symmetry phase of Dyson's hierarchical model*. United States. doi:10.1103/PhysRevD.61.114509.

```
Godina, J. J., Meurice, Y., and Oktay, M. B. Thu .
"Hyperscaling in the broken symmetry phase of Dyson's hierarchical model". United States. doi:10.1103/PhysRevD.61.114509.
```

```
@article{osti_20216473,
```

title = {Hyperscaling in the broken symmetry phase of Dyson's hierarchical model},

author = {Godina, J. J. and Meurice, Y. and Oktay, M. B.},

abstractNote = {We use polynomial truncations of the Fourier transform of the local measure to calculate the connected q-point functions of Dyson's hierarchical model in the broken symmetry phase. We show that accurate values of the connected one-, two-, and three-point functions can be obtained at large volume and in a limited range of constant external field coupled linearly to the field variable. We introduce a new method to obtain the correct infinite volume and zero external field extrapolations. We extract the leading critical exponents and show that they obey the scaling and hyperscaling relations with an accuracy ranging from 10{sup -5} to 5x10{sup -3}. We briefly discuss how to improve the method of calculation. (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevD.61.114509},

journal = {Physical Review. D, Particles Fields},

issn = {0556-2821},

number = 11,

volume = 61,

place = {United States},

year = {2000},

month = {6}

}