### Abstract

The renormalized coupling g_{R} 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 g_{R} in the lattice-regularized theory with the standard action for nearly thermodynamic lattices L/ξ∼7 and correlation lengths ξ 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 Lüscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S matrix is found.

Original language | English |
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Pages (from-to) | 1-11 |

Number of pages | 11 |

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

Volume | 60 |

Issue number | 9 |

Publication status | Published - Nov 1 1999 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics

### Cite this

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

*60*(9), 1-11.

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

Research output: Contribution to journal › Article

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 60, no. 9, pp. 1-11.

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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 - Seiler, Erhard

AU - Weisz, Peter

PY - 1999/11/1

Y1 - 1999/11/1

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 lattice-regularized theory with the standard action for nearly thermodynamic lattices L/ξ∼7 and correlation lengths ξ 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 Lüscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S 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 lattice-regularized theory with the standard action for nearly thermodynamic lattices L/ξ∼7 and correlation lengths ξ 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 Lüscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S matrix is found.

UR - http://www.scopus.com/inward/record.url?scp=17144382487&partnerID=8YFLogxK

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M3 - Article

AN - SCOPUS:17144382487

VL - 60

SP - 1

EP - 11

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 9

ER -