Category: Physics

Summary: Estimating critical dynamical behavior in a large two-dimensional Ising model by measuring long-run autocorrelation and fluctuation statistics near the critical temperature.

The two-dimensional Ising model is a standard testbed for phase transitions, and its static critical behavior is well understood. This experiment focuses instead on critical dynamics: how slowly the system relaxes under single-spin-flip updates when it is simulated very close to the critical temperature on a large lattice.

The script runs vectorized checkerboard Metropolis dynamics on a 1024 by 1024 grid, then measures magnetization, energy, and time-series correlations over very long trajectories. The main goal is to tighten estimates of the relaxation time and related observables using much deeper runs than short exploratory simulations usually provide.

That makes the experiment valuable as a precision dynamics study rather than a simple textbook reproduction. The long trajectories are designed to expose finite-size and finite-time effects that smaller or shallower simulations can miss.

Method: Large-scale checkerboard Metropolis simulation of a 1024 by 1024 Ising lattice at criticality, with long-run time-series analysis of magnetization and energy.

What is measured: Autocorrelation time, susceptibility, specific heat, mean absolute magnetization, magnetization squared, mean energy per spin, total sweeps, and number of measurements collected.