2D Ising Model (Metropolis)

Classical model of ferromagnetism. At T_c ≈ 2.269 (in units J/k_B), a spontaneous phase transition: ordered ↔ disordered. Exactly solved by Onsager (1944).

T_c ≈ 2.269 (Onsager exact)
|M| (magnetization): –
E (energy/spin): –
χ (susceptibility): –
MCS steps: 0
Metropolis rule: flip spin with probability min(1, e^{-ΔE/T}). Onsager (1944): exact T_c = 2/ln(1+√2) ≈ 2.269. At T_c: diverging correlation length, power-law spin clusters — critical universality class (2D Ising) with β=1/8, γ=7/4, ν=1.