2D Ising Model & Onsager Exact Solution

Monte Carlo simulation (Metropolis algorithm) with Onsager's exact 1944 solution overlay. Critical temperature Tc = 2/ln(1+√2) ≈ 2.269 (in units J/k_B).

Simulation

T/Tc: 1.01
|M|: 0.00
Energy/spin: 0.00
Onsager |M|: 0.00
Sweeps: 0
Metropolis rule:
ΔE=2J·sᵢ·Σneighbors
Accept if ΔE≤0, else
P=exp(-ΔE/kT)

Onsager 1944:
Tc=2/ln(1+√2)≈2.269
M=(1-sinh⁻⁴(2J/kT))^(1/8)

Critical exponent β=1/8
(M~|T-Tc|^β near Tc)