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Benford's law is an empirical law predicting the distribution of the firstsignificant digits of numbers obtained from natural phenomena and mathematicaltables. It has been found to be applicable for numbers coming from a plethoraof sources, varying from seismographic, biological, financial, to astronomical.We apply this law to analyze the data obtained from physical many-body systemsdescribed by the one-dimensional anisotropic quantum XY models in a transversemagnetic field. We detect the zero-temperature quantum phase transition andfind that our method gives better finite-size scaling exponents for thecritical point than many other known scaling exponents using measurablequantities like magnetization, entanglement, and quantum discord. We extend ouranalysis to the same system but at finite temperature and find that it alsodetects the finite temperature phase transition in the model. Moreover, wecompare the Benford distribution analysis with the same obtained from theuniform and Poisson distributions. The analysis is furthermore important inthat the high-precision detection of the cooperative physical phenomena ispossible even from low-precision experimental data.

Benford's law gives better scale exponents in phase transitions of quantum XY models