Pushing the limits of EPD zeros method

TL;DR

This paper investigates the robustness and parameter sensitivity of the energy probability distribution zeros method for studying phase transitions, proposing improvements to enhance convergence and accuracy with low computational cost.

Contribution

It explores optimal parameter choices for the EPD zeros method, demonstrates its robustness, and proposes solutions for convergence issues to improve phase transition analysis.

Findings

EPD zeros method is robust against parameter variations.

Small deviations in critical temperature estimates occur despite parameter changes.

Proposed algorithm modifications improve convergence and accuracy.

Abstract

The use of partition function zeros in the study of phase transition is growing in the last decade mainly due to improved numerical methods as well as novel formulations and analysis. In this paper the impact of different parameters choice for the energy probability distribution (EPD) zeros recently introduced by Costa et al is explored in search for optimal values. Our results indicate that the EPD method is very robust against parameter variations and only small deviations on estimated critical temperatures are found even for large variation of parameters, allowing to obtain accurate results with low computational cost. A proposal to circumvent potential convergence issues of the original algorithm is presented and validated for the case where it occurs.