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 φ44 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 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.

Keywords

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