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arXiv:1603.04928 · Computer Physics Communications

Energy probability distribution zeros: A route to study phase transitions

B. V. Costa, L. A. S. Mόl, J. C. S. Rocha

Published Mar 18, 2017• 24 citations
arXivHTMLPDF
DOI
10.1016/j.cpc.2017.03.003

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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.
Partition function zeros play a central role in the study of phase transitions. Recently, energy probability distribution (EPD) zeros were proposed as an alternative approach that solves some of the implementation issues present in the Fisher zeros method by allowing drastic reduction of the polynomial. Here, a formulation based on the EPD zeros that can reduce even more the polynomial degree while maintaining its accuracy is presented. This method has shown to be computationally cheaper than the EPD zeros, allowing the study of systems by using partition function zeros that would be unfeasible otherwise. In addition, the method can be easily extended to study phase transitions in external fields while maintaining all of its improvements.