title: Benford's law gives better scaling exponents in phase transitions of quantum XY models.
abstract: Benford's law is an empirical law predicting the distribution of the first significant digits of numbers obtained from natural phenomena and mathematical tables. It has been found to be applicable for numbers coming from a plethora of sources, varying from seismographic, biological, financial, to astronomical. We apply this law to analyze the data obtained from physical many-body systems described by the one-dimensional anisotropic quantum XY models in a transverse magnetic field. We detect the zero-temperature quantum phase transition and find that our method gives better finite-size scaling exponents for the critical point than many other known scaling exponents using measurable quantities like magnetization, entanglement, and quantum discord. We extend our analysis to the same system but at finite temperature and find that it also detects the finite-temperature phase transition in the model. Moreover, we compare the Benford distribution analysis with the same obtained from the uniform and Poisson distributions. The analysis is furthermore important in that the high-precision detection of the cooperative physical phenomena is possible even from low-precision experimental data.
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.
authors.forename: Ameya Deepak
authors.initials: AD
authors.lastname: Rane
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.
authors.forename: Utkarsh
authors.initials: U
authors.lastname: Mishra
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.
authors.forename: Anindya
authors.initials: A
authors.lastname: Biswas
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.
authors.forename: Aditi
authors.initials: A
authors.lastname: Sen De
authors.affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India.
authors.forename: Ujjwal
authors.initials: U
authors.lastname: Sen
mesh_terms: D016880:Anisotropy; D060526:Magnetic Fields; D008962:Models, Theoretical; D044367:Phase Transition; D011789:Quantum Theory; D013696:Temperature