Roughening
Transition
Crystal interface roughness W² = ⟨h²⟩ as function of T — smooth to rough transition at T_R
Temperature T/J
1.50
System size L
128
MC steps/frame
10
Reset
Scan T
Interface Height Profile h(x)
—
T
—
W² = ⟨h²⟩
—
Phase
—
MCS×10³
Roughness W²(T) vs Temperature
Below T_R: W² ~ const (smooth, logarithmic at most). Above T_R: W² ~ L² (rough, diverges with system size). T_R ≈ 2J/ln(1+√2) ≈ 1.13J (SOS model).