Ising Model Monte Carlo Simulation

Research question

How can Monte Carlo sampling reproduce the qualitative behavior of a two-dimensional Ising model near a phase transition?

Background

The Ising model is a compact route into statistical mechanics, numerical sampling, autocorrelation, and finite-size effects.

Mathematical model

The project tracks lattice size, spin states, coupling, temperature, boundary conditions, and observables such as energy, magnetization, heat capacity, and susceptibility.

Methods

The numerical work is organized around the sampling algorithm, burn-in, measurement interval, random seed strategy, and uncertainty estimates.

Implementation

The finished page should include commands for reproducing plots and benchmark runtimes for different lattice sizes.

Results

Expected outputs include magnetization curves, energy curves, snapshots at different temperatures, and finite-size comparisons.

Validation

Compare limiting cases, check thermalization, inspect autocorrelation, and compare critical behavior with known references.

Limitations

Small lattices and short chains can give visually persuasive but statistically weak conclusions.

What I learned

The project is useful for learning sampling, error bars, reproducibility, and the difference between visual and quantitative evidence.

Future work

Potential extensions include Wolff or Swendsen-Wang updates, finite-size scaling, and a browser-based visualization.