Scaling and density of Lee-Yang zeros in the four-dimensional Ising model

All of the information on the behavior of the four-dimensional Ising model is contained in the distribution and density of its partition function zeros. This model is believed to belong to the same universality class as the φ₄⁴ model which plays a central role in relativistic quantum field theory. Here the scaling behavior of the edge of the distribution of zeros and the asymptotic form for the density of zeros are determined. The finite-size dependency of the density of zeros—or the distance between zeros—at the infinite volume critical point is found using both analytic and numerical approaches. As with a previous analysis of the lowest lying zero, emphasis is laid on the multiplicative logarithmic corrections to mean field scaling behavior which are related to the triviality of the Ising and φ⁴ models in four dimensions.