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

The renormalized coupling \gr defined through the connected 4-point function at zero external momentum in the non-linear O(3) sigma-model in two dimensions, is computed in the continuum form factor bootstrap approach with estimated error

\sim 0.3%

. New high precision data are presented for \gr in the lattice regularized theory with standard action for nearly thermodynamic lattices

L/\xi\sim 7

and correlation lengths

\xi

up to

\sim 122

and with the fixed point action for correlation lengths up to

\sim 12

. The agreement between the form factor and lattice results is within

\sim 1%

. We also recompute the phase shifts at low energy by measuring the two-particle energies at finite volume, a task which was previously performed by L\"uscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S-matrix is found.

Note:

23 pages, 4 figures Report-no: AZPH-TH-99-03, BUTP-99-04, MPI-PhT/99-09

lattice field theory: action
bootstrap: form factor
sigma model: nonlinear
symmetry: O(3)
dimension: 2
coupling constant
n-point function
continuum limit
correlation: length
partial wave analysis

References(30)

Figures(0)

Continuum Limit and Improved Action in Lattice Theories. 1. Principles and $\varphi^4$ Theory

K. Symanzik
(
- DESY
)

- Nucl.Phys.B 226 (1983) 187-204
•
DOI:
- 10.1016/0550-3213(83)90468-6

Superinstantons and the reliability of perturbation theory in nonAbelian models

- Phys.Rev.Lett. 74 (1995) 1920-1923
•
e-Print:
- hep-lat/9311019
•
DOI:
- 10.1103/PhysRevLett.74.1920

Quantum Nonlocal Charges and Absence of Particle Production in the Two-Dimensional Nonlinear Sigma Model

M. Luscher
(
- Bohr Inst.
)

- Nucl.Phys.B 135 (1978) 1-19,
- Nucl.Phys.B135 (1978) 1-19 and Copenhagen Univ - NBI-HE-77-44 (77,REC.DEC) 40p
•
DOI:
- 10.1016/0550-3213(78)90211-0

Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models

- Annals Phys. 120 (1979) 253-291,
- Also in *Jimbo, M. (ed.): Yang-Baxter equation in integrable systems* 82-120, and in *Rebbi, C. (ed.), Soliani, G. (ed.): Solitons and Particles*, 446-484,
•
DOI:
- 10.1016/0003-4916(79)90391-9

Relativistic Factorized S Matrix in Two-Dimensions Having O(N) Isotopic Symmetry

- Nucl.Phys.B 133 (1978) 525,
- JETP Lett. 26 (1977) 457
•
DOI:
- 10.1016/0550-3213(78)90239-0

Exact Form-Factors in (1+1)-Dimensional Field Theoretic Models with Soliton Behavior

M. Karowski
(
- Freie U., Berlin
)
,
P. Weisz
(
- Freie U., Berlin
)

- Nucl.Phys.B 139 (1978) 455-476
•
DOI:
- 10.1016/0550-3213(78)90362-0

Perturbative versus nonperturbative QFT: Lessons from the O(3) NLS model

J. Balog
(
- Munich, Max Planck Inst.
)
,
M. Niedermaier
(
- Munich, Max Planck Inst.
)
,
T. Hauer
(
- MIT, LNS
)

- Phys.Lett.B 386 (1996) 224-232
•
e-Print:
- hep-th/9604161
•
DOI:
- 10.1016/0370-2693(96)00906-9

Off-shell dynamics of the O(3) NLS model beyond Monte Carlo and perturbation theory

- Nucl.Phys.B 500 (1997) 421-461
•
e-Print:
- hep-th/9612039
•
DOI:
- 10.1016/S0550-3213(97)00314-3

A Scaling hypothesis for the spectral densities in the O(3) nonlinear sigma model

- Phys.Rev.Lett. 78 (1997) 4151-4154
•
e-Print:
- hep-th/9701156
•
DOI:
- 10.1103/PhysRevLett.78.4151

Exact form-factors in integrable quantum field theories: The Sine-Gordon model

Hratchya M. Babujian
(
- Freie U., Berlin
)
,
A. Fring
(
- Freie U., Berlin
)
,
M. Karowski
(
- Freie U., Berlin
)
,
A. Zapletal
(
- Freie U., Berlin
)

- Nucl.Phys.B 538 (1999) 535-586
•
e-Print:
- hep-th/9805185
•
DOI:
- 10.1016/S0550-3213(98)00737-8

How to Calculate the Elastic Scattering Matrix in Two-dimensional Quantum Field Theories by Numerical Simulation

Martin Luscher
(
- DESY
)
,
Ulli Wolff
(
- Kiel U. and
- Bielefeld U.
)

- Nucl.Phys.B 339 (1990) 222-252
•
DOI:
- 10.1016/0550-3213(90)90540-T

Perfect lattice action for asymptotically free theories

P. Hasenfratz
(
- Bern U.
)
,
F. Niedermayer
(
- Bern U.
)

- Nucl.Phys.B 414 (1994) 785-814
•
e-Print:
- hep-lat/9308004
•
DOI:
- 10.1016/0550-3213(94)90261-5

The Exact mass gap of the O(3) and O(4) nonlinear sigma models in d = 2

- Phys.Lett.B 245 (1990) 522-528
•
DOI:
- 10.1016/0370-2693(90)90685-Y

Nonlinear sigma model, form-factors and universality

- Phys.Lett.B 445 (1998) 160-164
•
e-Print:
- hep-th/9809154
•
DOI:
- 10.1016/S0370-2693(98)01425-7

Four point renormalized coupling constant and Callan-Symanzik Beta function in O(N) models

Andrea Pelissetto
(
- Pisa U. and
- INFN, Pisa
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

- Nucl.Phys.B 519 (1998) 626-660
•
e-Print:
- cond-mat/9711078
•
DOI:
- 10.1016/S0550-3213(98)00164-3

A Monte Carlo Simulation With an 'Improved' Action for the O(3) Nonlinear $\sigma$ Model

M. Falcioni
(
- Rome U. and
- INFN, Rome
)
,
G. Martinelli
(
- Frascati
)
,
M.L. Paciello
(
- INFN, Rome
)
,
B. Taglienti
(
- INFN, Rome
)
,
G. Parisi
(
- Rome U., Tor Vergata
)

- Nucl.Phys.B 225 (1983) 313-325
•
DOI:
- 10.1016/0550-3213(83)90414-5

Four point renormalized coupling constant in O(N) models

Massimo Campostrini
(
- Pisa U. and
- INFN, Pisa
)
,
Andrea Pelissetto
(
- Pisa U. and
- INFN, Pisa
)
,
Paolo Rossi
(
- Pisa U. and
- INFN, Pisa
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

- Nucl.Phys.B 459 (1996) 207-242
•
e-Print:
- hep-lat/9506002
•
DOI:
- 10.1016/0550-3213(95)00569-2

Four point renormalized coupling constant in O(N) models

- Nucl.Phys.B Proc.Suppl. 47 (1996) 751-754,
- Lattice 1995:0751-754,
- In *Melbourne 1995, Proceedings, Lattice '95* 751-754, and Preprint - Campostrini, M. (rec.Sep.95) 4 p
•
e-Print:
- hep-lat/9509005
•
DOI:
- 10.1016/0920-5632(96)00166-1

On the evaluation of universal nonperturbative constants in O(N) sigma models

Massimo Campostrini
(
- Pisa U. and
- INFN, Pisa
)
,
Andrea Pelissetto
(
- Pisa U. and
- INFN, Pisa
)
,
Paolo Rossi
(
- Pisa U. and
- INFN, Pisa
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

- Phys.Lett.B 402 (1997) 141-146
•
e-Print:
- hep-lat/9702010
•
DOI:
- 10.1016/S0370-2693(97)00456-5

Perturbative renormalization group, exact results and high temperature series to order 21 for the N vector spin models on the square lattice

P. Butera
(
- INFN, Milan and
- Milan U.
)
,
M. Comi
(
- INFN, Milan and
- Milan U.
)

- Phys.Rev.B 54 (1996) 15828-15848
•
e-Print:
- hep-lat/9710092
•
DOI:
- 10.1103/PhysRevB.54.15828

High temperature study of the Kosterlitz-Thouless phase transition in the XY model on the triangular lattice

P. Butera
(
- INFN, Milan and
- Milan U.
)
,
M. Comi
(
- INFN, Milan and
- Milan U.
)

- Phys.Rev.B 50 (1994) 3052-3057
•
e-Print:
- cond-mat/9902326
•
DOI:
- 10.1103/PhysRevB.50.3052

Renormalized couplings and scaling correction amplitudes in the N vector spin models on the sc and the bcc lattices

P. Butera
(
- INFN, Milan and
- Milan U.
)
,
M. Comi
(
- INFN, Milan and
- Milan U.
)

- Phys.Rev.B 58 (1998) 11552-11569
•
e-Print:
- hep-lat/9805025
•
DOI:
- 10.1103/PhysRevB.58.11552

A Strong coupling analysis of two-dimensional O(N) sigma models with N<=2 on square, triangular and honeycomb lattices

Massimo Campostrini
(
- Pisa U. and
- INFN, Pisa
)
,
Andrea Pelissetto
(
- Pisa U. and
- INFN, Pisa
)
,
Paolo Rossi
(
- Pisa U. and
- INFN, Pisa
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

- Phys.Rev.B 54 (1996) 7301-7317
•
e-Print:
- hep-lat/9603002
•
DOI:
- 10.1103/PhysRevB.54.7301

A Strong coupling analysis of two-dimensional O(n) sigma models with N >= 3 on square, triangular and honeycomb lattices

Massimo Campostrini
(
- Pisa U. and
- INFN, Pisa
)
,
Andrea Pelissetto
(
- Pisa U. and
- INFN, Pisa
)
,
Paolo Rossi
(
- Pisa U. and
- INFN, Pisa
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

- Phys.Rev.D 54 (1996) 1782-1808
•
e-Print:
- hep-lat/9602011
•
DOI:
- 10.1103/PhysRevD.54.1782

Strong coupling expansion of lattice O(N) sigma models

Massimo Campostrini
(
- Pisa U. and
- INFN, Pisa
)
,
Andrea Pelissetto
(
- Pisa U. and
- INFN, Pisa
)
,
Paolo Rossi
(
- Pisa U. and
- INFN, Pisa
)
,
Ettore Vicari
(
- Pisa U. and
- INFN, Pisa
)

- Nucl.Phys.B Proc.Suppl. 47 (1996) 755-758,
- Lattice 1995:0755-758,
- In *Melbourne 1995, Proceedings, Lattice '95* 755-758, and Pisa U. - IFUP-TH-95-51 (95,rec.Sep.) 4 p
•
e-Print:
- hep-lat/9509025
•
DOI:
- 10.1016/0920-5632(96)00167-3

1-25 of 30
1
2
25 / page