2D Ising Model - Phase Transition & Critical Temperature

Lattice Size (L × L)

50 × 50

Temperature (T/T_c)

1.00 (T_c ≈ 2.27)

External Field (H)

0.0

Coupling Constant (J)

1.0

Random

All Spins Up

All Spins Down

Steps per Frame

1000

Energy per spin:

H = -J Σ s_i s_j - H Σ s_i

Metropolis acceptance probability:

P = min(1, e^{-ΔE/T})

Critical temperature: T_c ≈ 2.269 (in units J/k_B)

Spin Up (+1)

Spin Down (-1)

|Magnetization|

Energy

Magnetization |M|

0.00

Energy per Spin

0.00

Temperature T

2.27

Monte Carlo Steps

Critical Region

Near T_c: Fluctuations dominate, critical phenomena observed

Susceptibility: - Specific Heat: -