Open AccessThe impact of fluctuations on the zeros of the energy probability distribution
Author(s) -
R. G. M. Rodrigues,
L. A. S. Mól
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1483/1/012007
Subject(s) - mathematics , monte carlo method , polynomial , histogram , zero (linguistics) , statistical physics , plane (geometry) , probability distribution , complex plane , phase transition , distribution (mathematics) , energy (signal processing) , zero point energy , mathematical analysis , statistics , physics , computer science , geometry , quantum mechanics , philosophy , artificial intelligence , image (mathematics) , linguistics
In this communication we explore the possible effects of statistical fluctuations on the use of the Energy Probability Distribution (EPD) zeros to study phase transitions. In the EPD zeros technique one has to find the roots of a polynomial whose coefficients are given by the EPD - a histogram of energy values obtained in a Monte Carlo simulation, for example. Phase transitions are signalized by the presence of a zero that approaches the point (1,0) in the complex plane. Once the EPD estimations are usually subject to statistical fluctuations and polynomial roots are known to be sensitive to modifications in its coefficients, we have compared the roots of a given polynomial with the roots of a perturbed one, searching for possible impacts on the method. Our results show that although the overall map of zeros is modified, the location of the dominant zero, the one that indicates the presence of a phase transition, is not affected. Indeed, even for 30% perturbation only small modifications in the dominant zero location is observed.