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Journal of Physics A Mathematical and General

Amplitude-exponent relation for the correlation length in the spherical model

Malte Henkel

Published Feb 21, 1988• 15 citations
Publisher

Abstract

For the critical spherical model in d=r+1 dimensions, finite-size calculations of the spin-spin and energy-energy correlation lengths suggest relations among the critical exponents and the finite-size scaling amplitudes of the correlation lengths similar to those obtained in (1+1) dimensions from conformal invariance. For antiperiodic boundary conditions, the results agree with numerical studies in the (2+1)-dimensional Ising model.

DOI
10.1088/0305-4470/21/4/007

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For the critical spherical model in d=r+1 dimensions, finite-size calculations of the spin-spin and energy-energy correlation lengths suggest relations among the critical exponents and the finite-size scaling amplitudes of the correlation lengths similar to those obtained in (1+1) dimensions from conformal invariance. For antiperiodic boundary conditions, the results agree with numerical studies in the (2+1)-dimensional Ising model.
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Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems S d − 1 × of arbitrary dimensionality d . Numerical studies have up to now been unable to validate this result due to the intricacies of lattice discretisation of such curved spaces. We present a cluster-update Monte Carlo study of the Ising model on a three-dimensional geometry using slightly irregular lattices that confirms the validity of a linear amplitude-exponent relation to high precision.