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

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 ${\varphi }_4^4$ scalar 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 ${\varphi }_4^4$ 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.

arXiv comment12 pages, 6 figures, 6 tables

References in corpus (8)

• Scaling Relations for Logarithmic Corrections
• Renormalization Group Analysis of Finite-Size Scaling in the ${\Phi }_4^4$ Model
• The four dimensional site-diluted Ising model: a finite-size scaling study
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• Logarithmic Corrections for Spin Glasses, Percolation and Lee-Yang Singularities in Six Dimensions
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• Revisiting (logarithmic) scaling relations using renormalization group
• Revising the universality class of the four-dimensional Ising model

Cited by in corpus (2)

• Critical and tricritical behavior of the $d=3$ Blume-Capel model: Results from small-scale Monte Carlo simulations
• Phase transition properties via partition function zeros: The Blume-Capel ferromagnet revisited