2D Ising Model — Metropolis

Parameters

Temperature T2.27

Tc ≈ 2.269 (Onsager exact)

Observables

|Magnetization| ⟨|m|⟩—

Energy per spin ⟨e⟩—

Accept rate—

Sweeps—

Phase—

Theory

The 2D Ising model exhibits a second-order phase transition. Below Tc, spontaneous magnetization emerges. Metropolis algorithm: flip spin i with probability min(1, e^{−ΔE/T}). Onsager (1944) gave the exact solution: Tc = 2J/ln(1+√2) ≈ 2.269.