Revisiting the Lee-Yang singularities in the four-dimensional Ising model: a tribute to the memory of Ralph Kenna

J. J. Ruiz-Lorenzo

doi:10.5488/cmp.27.33604

Authors

J. J. Ruiz-Lorenzo Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, 06006 Badajoz, Spain https://orcid.org/0000-0003-0551-9891

DOI:

https://doi.org/10.5488/cmp.27.33604

Keywords:

renormalization group, scaling, logarithms, mean field, complex singularities

Abstract

We have studied numerically the Lee-Yang singularities of the four dimensional Ising model at criticality, which is believed to be in the same universality class as the φ₄⁴scalar field theory. We have focused in the numerical characterization of the logarithmic corrections to the scaling of the zeros of the partition function and its cumulative probability distribution, finding a very good agreement with the predictions of the renormalization group computation on the φ₄⁴ scalar field theory. To obtain these results, we have extended a previous study [R. Kenna, C. B. Lang, Nucl. Phys., 1993, B393, 461] in which there were computed numerically the first two zeros for L≤24 lattices, to the computation of the first four zeros for L≤64 lattices.

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