Computational Methods for Phase Transitions

Implement the Metropolis Monte Carlo algorithm to simulate the 2D Ising model.

Observe critical slowing down in simulations and explain its origin from the diverging correlation time.

Describe a cluster algorithm (e.g., Wolff) and explain how it mitigates critical slowing down.

Apply the histogram reweighting technique to extrapolate simulation results to nearby temperatures from a single run.

State the finite-size scaling ansatz for thermodynamic observables like magnetization and susceptibility.

Use the Binder cumulant method to accurately locate the critical temperature from simulations on different system sizes.

Extract critical exponent ratios (e.g., β/ν, γ/ν) by performing a data collapse using the finite-size scaling ansatz.