Monte Carlo simulation of ferromagnetism and phase transitions
Energy: —
Magnetization: —
T: 2.27
Temperature (kT/J)2.27 (T_c)
External Field (h)0
Speed8
The 2D Ising model is the paradigm of statistical mechanics phase transitions. Each site σᵢ ∈ {±1} (spin up/down). The Hamiltonian is H = −J Σᵢⱼ σᵢσⱼ − h Σᵢ σᵢ. Below the Curie temperature T_c ≈ 2.269 J/k (Onsager 1944), the system spontaneously magnetizes. At T_c, correlations become long-range and the system is scale-invariant (conformal field theory). Monte Carlo uses the Metropolis algorithm: flip spin i with probability min(1, e^(−ΔE/kT)).