Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105

Sergio Caracciolo; Robert G. Edwards; Andrea Pelissetto; Alan D. Sokal

doi:10.1103/PhysRevLett.75.1891

Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105

Sergio Caracciolo, Robert G. Edwards, Andrea Pelissetto, Alan D. Sokal

Research output: Contribution to journal › Article › peer-review

Abstract

We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.

Original language	English (US)
Pages (from-to)	1891-1894
Number of pages	4
Journal	Physical Review Letters
Volume	75
Issue number	10
DOIs	https://doi.org/10.1103/PhysRevLett.75.1891
State	Published - 1995

ASJC Scopus subject areas

General Physics and Astronomy

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10.1103/PhysRevLett.75.1891

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title = "Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105",

abstract = "We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.",

author = "Sergio Caracciolo and Edwards, {Robert G.} and Andrea Pelissetto and Sokal, {Alan D.}",

year = "1995",

doi = "10.1103/PhysRevLett.75.1891",

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AU - Caracciolo, Sergio

AU - Edwards, Robert G.

AU - Pelissetto, Andrea

AU - Sokal, Alan D.

PY - 1995

Y1 - 1995

N2 - We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.

AB - We carry out a high-precision Monte Carlo simulation of the two-dimensional O(3)-invariant σ model at correlation lengths ξ up to ∼105. Our work employs a powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is 25% at ξ∼102, decreases to 4% at ξ∼105.

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JO - Physical Review Letters

JF - Physical Review Letters

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Asymptotic scaling in the two-dimensional O(3) σ model at correlation length 105

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