Universal amplitude-exponent relation for the Ising model on sphere-like lattices

Abstract

Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times \mathbb{R}$ 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.

6 pages, 2 figures, Europhys. Lett., in print

References in corpus (1)

• Monte Carlo study of the scaling of universal correlation lengths in three-dimensional O(n) spin models

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