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Finite size scaling at zeta/L much larger than 1

Sergio Caracciolo
(
- Salento U. and
- INFN, Lecce
)
,
Robert G. Edwards
(
- Florida State U., SCRI
)
,
Sabino Jose Ferreira
(
- Minas Gerais U.
)
,
Andrea Pelissetto
(
- New York U.
)
,
Alan D. Sokal
(
- New York U.
)

Sep, 1994

11 pages

Published in:

Phys.Rev.Lett. 74 (1995) 2969-2972

e-Print:

hep-lat/9409004 [hep-lat]

DOI:

10.1103/PhysRevLett.74.2969

Report number:

NYU-TH-94-09-02,
FSU-SCRI-94-86

View in:

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Abstract: (DESY)

We present a simple and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully its systematic and statistical errors, and we illustrate it using three examples: the two-dimensional three-state Potts antiferromagnet on the square lattice, and the two-dimensional

O(3)

and

O(\infty)

\sigma

-models. In favorable cases it is possible to obtain reliable extrapolations (errors of a few percent) even when the correlation length is 1000 times larger than the lattice.

Note:

*Title changed in the journal*

scaling: finite size
lattice field theory
Potts model
dimension: 2
sigma model: O(infinity)
symmetry: O(3)
correlation: length
numerical calculations: Monte Carlo

References(10)

Figures(0)

A Numerical method to compute the running coupling in asymptotically free theories

Martin Luscher
(
- DESY
)
,
Peter Weisz
(
- Munich, Max Planck Inst.
)
,
Ulli Wolff
(
- CERN
)

- Nucl.Phys.B 359 (1991) 221-243
•
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An Application of finite size scaling to Monte Carlo simulations

Jae-Kwon Kim
(
- Arizona U.
)

- Phys.Rev.Lett. 70 (1993) 1735-1738
•
DOI:
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- Nucl.Phys.B 34 702

Finite Size Effects in Massive Field Theory

Herbert Neuberger
(
- Rutgers U., Piscataway
)

- Phys.Lett.B 233 (1989) 183-186
•
DOI:
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- Proc.Roy.Soc.Lond.A 383 43

Antiferromagnetic Potts models

Jian-Sheng Wang
(
- Rutgers U., Piscataway
)
,
Robert H. Swendsen
(
- Carnegie Mellon U. and
- Rutgers U., Piscataway
)
,
Roman Kotecky
(
- Charles U.
)

- Phys.Rev.Lett. 63 (1989) 109-112
•
DOI:
- 10.1103/PhysRevLett.63.109

Three-state antiferromagnetic Potts models: A Monte Carlo study

Jian-Sheng Wang
(
- Julich, Forschungszentrum
)
,
Robert H. Swendsen
(
- Carnegie Mellon U.
)
,
Roman Kotecky
(
- Charles U.
)

- Phys.Rev.B 42 (1990) 2465-2474
•
DOI:
- 10.1103/PhysRevB.42.2465

Comment on `Antiferromagnetic Potts models'

Mona Lubin
(
- New York U.
)
,
Alan D. Sokal
(
- New York U.
)

- Phys.Rev.Lett. 71 (1993) 1778
•
e-Print:
- hep-lat/9304002
•
DOI:
- 10.1103/PhysRevLett.71.1778

Collective Monte Carlo Updating for Spin Systems

Ulli Wolff
(
- Kiel U.
)

- Phys.Rev.Lett. 62 (1989) 361
•
DOI:
- 10.1103/PhysRevLett.62.361

Nonuniversal critical dynamics in Monte Carlo simulations

Robert H. Swendsen
(
- Carnegie Mellon U. and
- Georgia U.
)
,
Jian-Sheng Wang
(
- Carnegie Mellon U.
)

- Phys.Rev.Lett. 58 (1987) 86-88
•
DOI:
- 10.1103/PhysRevLett.58.86