Crystal Surface Roughening Transition

SOS (solid-on-solid) model: below T_R, surface is smooth (faceted); above T_R, interface width W ~ L diverges. Monte Carlo simulation reveals the roughening transition and logarithmic growth of W²(T).

Temperature T/T_R: 0.8

System size L: 64

MC steps/frame: 200

T/T_R = 0.80

W² = — (roughness)

Phase: —

⟨h⟩ = —

Max step: —

SOS energy: E = J·Σ|h_i−h_j|
T_R = 2J/ln(2+√3) ≈ 1.135J

Smooth phase: W² → const
Rough phase: W² ~ log(L)
BKT-type transition!

W² vs T — shows roughening transition at T_R