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Benford's law is an empirical edict stating that the lower digits appear moreoften than higher ones as the first few significant digits in statistics ofnatural phenomena and mathematical tables. A marked proportion of such analysesis restricted to the first significant digit. We employ violation of Benford'slaw, up to the first four significant digits, for investigating magnetizationand correlation data of paradigmatic quantum many-body systems to detectcooperative phenomena, focusing on the finite-size scaling exponents thereof.We find that for the transverse field quantum XY model, behavior of the veryfirst significant digit of an observable, at an arbitrary point of theparameter space, is enough to capture the quantum phase transition in the modelwith a relatively high scaling exponent. A higher number of significant digitsdo not provide an appreciable further advantage, in particular, in terms of anincrease in scaling exponents. Since the first significant digit of a physicalquantity is relatively simple to obtain in experiments, the results havepotential implications for laboratory observations in noisy environments.

physics letters a

Benford analysis of quantum critical phenomena: First digit provides  high finite-size scaling exponent while first two and further are not much  better