Zipf's law in Nuclear Multifragmentation and Percolation Theory

TL;DR

This paper analyzes the distribution of nuclear fragment sizes near the critical point, showing Zipf's Law does not apply and proposing Zipf-Mandelbrot distributions as a better fit, with implications for identifying critical points.

Contribution

It demonstrates that Zipf's Law does not describe nuclear fragment distributions at criticality and introduces Zipf-Mandelbrot distributions as a more accurate model.

Findings

Zipf's Law does not hold for nuclear fragment sizes.

Zipf-Mandelbrot distributions better fit the data.

Rank-ordered distributions can indicate critical points.

Abstract

We investigate the average sizes of the $n$ largest fragments in nuclear multifragmentation events near the critical point of the nuclear matter phase diagram. We perform analytic calculations employing Poisson statistics as well as Monte Carlo simulations of the percolation type. We find that previous claims of manifestations of Zipf's Law in the rank-ordered fragment size distributions are not born out in our result, neither in finite nor infinite systems. Instead, we find that Zipf-Mandelbrot distributions are needed to describe the results, and we show how one can derive them in the infinite size limit. However, we agree with previous authors that the investigation of rank-ordered fragment size distributions is an alternative way to look for the critical point in the nuclear matter diagram.