Critical Dynamics of the 2D Ising Model: A Comparison of Correlation Time Definitions under Metropolis Dynamics

This repository contains the article and the complete set of numerical data and source codes used to study the critical dynamics of the two-dimensional Ising model at the critical temperature. Monte Carlo simulations using local Metropolis dynamics were performed for several lattice sizes. Two widely used definitions of the correlation time of the magnetization were systematically compared: the correlation time defined by the 1/e criterion and the integrated correlation time. The results confirm the presence of critical slowing down and highlight significant differences in the statistical stability of the two estimators under finite-size and finite-sampling conditions. Independent implementations in Python and C++ are provided to ensure numerical consistency and full reproducibility. The repository includes:- The full manuscript in PDF format- Reproducible simulation codes (Python and C++)- Raw and processed data files- Scripts for data analysis and figure generation This dataset serves as a reproducible baseline for comparisons with alternative dynamics, non-local algorithms, or hybrid Monte Carlo approaches in critical systems.