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