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

Martin Weigel·Wolfhard Janke
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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.

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Martin Weigel, Wolfhard Janke. 2000-08-20. Universal amplitude-exponent relation for the Ising model on sphere-like lattices. https://doi.org/10.1209/epl%2Fi2000-00377-0

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