Temperature T (J/k)2.269 (Tc)
Lattice size80
MC steps/frame5
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At Tc ≈ 2.269 J/k, the 2D Ising model undergoes a second-order phase transition — scale-free clusters and diverging correlation length.
Metropolis algorithm: flip spin with probability min(1, exp(−ΔE/T)). At Tc: correlation length ξ → ∞, clusters at all scales (fractal dimension df ≈ 1.875). Critical slowing down: autocorrelation time τ ~ ξ^z, z ≈ 2.17.