Dr Soumyajyoti Biswas, Assistant Professor in the Department of Physics, along with his Doctoral Scholar, Mr Soumyaditya Das, have presented groundbreaking findings through their research work titled “Critical Scaling through Gini Index”. The research paper was featured in the prestigious Physical Review Letters, which has an impact factor of 9.161.
In the systems showing critical behaviour, various response functions have a singularity at the critical point. Therefore, as the driving field is tuned toward its critical value, the response functions change drastically, typically diverging with universal critical exponents. In this Letter, 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 imminent criticality. This could be useful in many systems, including 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 the square lattice, and the fibre bundle model of fracture.
Fig.1: Shows the crossing point of the Gini index and the Kolkata index prior to critical point for three different models (from left Ising model in 2d, site percolation in 2d and fiber bundle model of fracture) form both side of critical point.
Collaborations and Future Plans
This work essentially builds a framework for indicating imminent critical points for any system. Therefore, in situations where such knowledge is vital, for example, in the fracture of solids, the method is going to be highly useful in forecasting the failure point. We are in the process of working with our collaborators at the University of Barcelona to experimentally verifying our methods for the compressive failure of porous samples. This is a significant first step towards opening new pathways in forecasting fracture points in disordered materials that could have an impact on laboratory-scale fractures to large constructions and eventually to earthquakes.
We wish the teacher-student duo many more fulfilling and enriching research endeavours in future!