Critical scaling through Gini index

TL;DR

This paper introduces a novel approach to analyze critical phenomena by using economic inequality measures like the Gini index to quantify response function scaling, simplifying the identification of critical points across various systems.

Contribution

It demonstrates that the Gini index captures universal critical scaling behavior, providing a simplified single-parameter fit for critical phenomena and a potential early warning indicator.

Findings

Gini index exhibits singularity at critical points.

Kolkata index crosses Gini index near criticality.

Method validated with Monte Carlo simulations on multiple models.

Abstract

In the systems showing critical behavior, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned towards its critical value, the response functions change drastically, typically diverging with universal critical exponents. In this work, we quantify the inequality of response functions with measures traditionally used in economics, namely by constructing a Lorenz curve and calculating the corresponding Gini index. The scaling of such a response function, when written in terms of the Gini index, shows singularity at a point that is at least as universal as the corresponding critical exponent. The critical scaling, therefore, becomes a single parameter fit, which is a considerable simplification from the usual form where the critical point and critical exponents are independent. We also show that another measure of inequality, the Kolkata index, crosses the Gini index at a point just prior to the critical point. Therefore, monitoring these two inequality indices for a system where the critical point is not known, can produce a precursory signal for the imminent criticality. This could be useful in many systems, including that in condensed matter, bio- and geophysics to atmospheric physics. The generality and numerical validity of the calculations are shown with the Monte Carlo simulations of the two dimensional Ising model, site percolation on square lattice and the fiber bundle model of fracture.