Monte Carlo Simulations for the Two-dimensional O(3) Nonlinear $\sigma$ Model

Martinelli, G.; Parisi, G.; Petronzio, R.

doi:10.1016/0370-2693(81)90610-9

Monte Carlo Simulations for the Two-dimensional O(3) Nonlinear $\sigma$ Model

G. Martinelli
(
- CERN
)
,
G. Parisi
(
- Rome U. and
- Frascati
)
,
R. Petronzio
(
- CERN
)

Dec, 1980

4 pages

Published in:

Phys.Lett.B 100 (1981) 485-488

Published: 1981

DOI:

10.1016/0370-2693(81)90610-9

Report number:

CERN-TH-3000

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Abstract: (Elsevier)

We report on the results of Monte Carlo simulations for the two-dimensional O(3) non-linear sigma model. The estimates based on the combined use of the renormalization group and of the high temperature expansion are found to be in agreement with our “data”. We present good experimental evidence for the absence of any phase transition, as expected on theoretical grounds.

LATTICE FIELD THEORY
FIELD THEORETICAL MODEL: SIGMA
FIELD THEORY: NONLINEAR
FIELD THEORY: O(3)
FIELD THEORY: TWO-DIMENSIONAL
RENORMALIZATION GROUP
PERTURBATION THEORY: STRONG COUPLING
STRONG COUPLING: PERTURBATION THEORY
FIELD THEORY: CRITICAL PHENOMENA
NUMERICAL CALCULATIONS: MONTE CARLO

References(9)

Figures(0)

Renormalization of the nonlinear sigma model in 2 + epsilon dimensions. Application to the Heisenberg ferromagnets

E. Brezin
(
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)
,
Jean Zinn-Justin
(
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)

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•
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Phase Transition in the Nonlinear $\sigma$ Model in 2 + $\epsilon$ Dimensional Continuum

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•
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Properties of the Two-dimensional O( $N$ ) $\sigma$ Models and the High Temperature Expansion

G. Parisi
(
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)

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•
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•
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Asymptotic Freedom Scales

Michael Creutz
(
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)

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•
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Monte Carlo Simulations for the Two-dimensional O(3) Nonlinear σ\sigmaσ Model

Citations per year

Renormalization of the nonlinear sigma model in 2 + epsilon dimensions. Application to the Heisenberg ferromagnets

Phase Transition in the Nonlinear σ\sigmaσ Model in 2 + ϵ\epsilonϵ Dimensional Continuum

The Phases of Two-dimensional Heisenberg Spin Systems From Strong Coupling Expansions

Properties of the Two-dimensional O(NNN) σ\sigmaσ Models and the High Temperature Expansion

Equation of state calculations by fast computing machines

Asymptotic Freedom Scales

Monte Carlo Simulations for the Two-dimensional O(3) Nonlinear $\sigma$ Model

Phase Transition in the Nonlinear $\sigma$ Model in 2 + $\epsilon$ Dimensional Continuum

Properties of the Two-dimensional O( $N$ ) $\sigma$ Models and the High Temperature Expansion