### Abstract

The renormalized coupling gR defined through the connected four-point function at zero external momentum in the nonlinear O(3) sigma model in two dimensions is computed in the continuum form factor bootstrap approach with an estimated error -0.3%. New high precision data are presented for gR in the latticeregularized theory with the standard action for nearly thermodynamic lattices L/£-7 and correlation lengths f up to - 122 and with the fixed point action for correlation lengths up to -12. The agreement between the form factor and lattice results is within -1%. We also recompute the phase shifts at low energy by measuring two-particle energies at finite volume, a task which was previously performed by Liischer and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov 5 matrix is found.

Original language | English |
---|---|

Article number | 094508 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 60 |

Issue number | 9 |

Publication status | Published - 1999 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*60*(9), [094508].

**Comparison of the O(3) bootstrap σ model with lattice regularization at low energies.** / Balog, J.; Niedermaier, Max; Niedermayer, Ferenc; Patrascioiu, Adrian; Sciler, Erhard; Weisz, Peter.

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 60, no. 9, 094508.

}

TY - JOUR

T1 - Comparison of the O(3) bootstrap σ model with lattice regularization at low energies

AU - Balog, J.

AU - Niedermaier, Max

AU - Niedermayer, Ferenc

AU - Patrascioiu, Adrian

AU - Sciler, Erhard

AU - Weisz, Peter

PY - 1999

Y1 - 1999

N2 - The renormalized coupling gR defined through the connected four-point function at zero external momentum in the nonlinear O(3) sigma model in two dimensions is computed in the continuum form factor bootstrap approach with an estimated error -0.3%. New high precision data are presented for gR in the latticeregularized theory with the standard action for nearly thermodynamic lattices L/£-7 and correlation lengths f up to - 122 and with the fixed point action for correlation lengths up to -12. The agreement between the form factor and lattice results is within -1%. We also recompute the phase shifts at low energy by measuring two-particle energies at finite volume, a task which was previously performed by Liischer and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov 5 matrix is found.

AB - The renormalized coupling gR defined through the connected four-point function at zero external momentum in the nonlinear O(3) sigma model in two dimensions is computed in the continuum form factor bootstrap approach with an estimated error -0.3%. New high precision data are presented for gR in the latticeregularized theory with the standard action for nearly thermodynamic lattices L/£-7 and correlation lengths f up to - 122 and with the fixed point action for correlation lengths up to -12. The agreement between the form factor and lattice results is within -1%. We also recompute the phase shifts at low energy by measuring two-particle energies at finite volume, a task which was previously performed by Liischer and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov 5 matrix is found.

UR - http://www.scopus.com/inward/record.url?scp=33750232084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33750232084&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33750232084

VL - 60

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 9

M1 - 094508

ER -