T_c = 2J/ln(1+√2) ≈ 2.269

2D Ising Model

Onsager exact solution · Metropolis-Hastings · 256×256

Temperature

T = 2.269

Color Scheme

Simulation Speed

20 sweeps

Initialize

Left-click: paint +1
Right-click: paint −1
Onsager (1944):
M = (1−sinh⁻⁴(2/T))^(1/8)
for T < T_c

Universality class: 2D Ising
β = 1/8, ν = 1, η = 1/4
|M| =
E/N =
FPS =
Sweeps = 0
Magnetization |M| history (last 200 frames)

Phase Diagram

── Onsager exact (orange)
• Simulation (red, 1s avg)

Phase Info