Scaling and Density of Lee-Yang Zeroes in the Four Dimensional Ising Model

TL;DR

This paper investigates the scaling behavior of Lee-Yang zeroes in the four-dimensional Ising model, revealing logarithmic corrections in finite-size systems and connecting these findings to critical phenomena in quantum field theory.

Contribution

It provides an analysis of the finite-size scaling and density of Lee-Yang zeroes in the 4D Ising model, highlighting logarithmic corrections and their implications.

Findings

Logarithmic corrections appear in finite-size scaling of Lee-Yang zeroes.

The density of zeroes aligns with susceptibility and specific heat scaling.

Analytical and numerical methods confirm the scaling behavior.

Abstract

The scaling behaviour of the edge of the Lee--Yang zeroes in the four dimensional Ising model is analyzed. This model is believed to belong to the same universality class as the $\phi^4_4$ model which plays a central role in relativistic quantum field theory. While in the thermodynamic limit the scaling of the Yang--Lee edge is not modified by multiplicative logarithmic corrections, such corrections are manifest in the corresponding finite--size formulae. The asymptotic form for the density of zeroes which recovers the scaling behaviour of the susceptibility and the specific heat in the thermodynamic limit is found to exhibit logarithmic corrections too. The density of zeroes for a finite--size system is examined both analytically and numerically.