Finding the Dominant Zero of the Energy Probability Distribution

TL;DR

This paper introduces an improved method for locating the dominant zero of the Energy Probability Distribution, significantly reducing computational time and increasing accuracy in studying phase transitions, exemplified on the 2D Ising model.

Contribution

The paper presents a novel technique that enhances the EPD zeros method by reducing processing time and improving accuracy for phase transition analysis.

Findings

Significant reduction in computational time for large lattices.

Enhanced accuracy in predicting thermodynamic limit properties.

Successful application to the 2D Ising model with results matching known solutions.

Abstract

In this work, we present a method to locate the dominant zero of the Energy Probability Distribution (EPD) Zeros method applied to the study of phase transitions. The technique strongly reduces computer processing time and also increases the accuracy of the results. As an example, we apply it to the 2D Ising model, comparing with both the exact Onsager's results and the previous EPD zeros method results. We show that, for large lattices, the processing time is drastically reduced when compared to other EPD zeros search procedures, whereas for small lattices the gain in accuracy allows very accurate predictions in the thermodynamic limit.