The impact of fluctuations on the zeros of the energy probability distribution

Abstract

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.

Pushing the limits of EPD zeros method

“…Iter (Normalized to 1) the zero closest to the point (1, 0). With that said, in a previous study [14], it was observed that the dominant zero is stable to random perturbations in the polynomial coefficients, i.e., applying a perturbation in the EPD following the equation,…”