Topological Defects: Vortices in 2D XY Model
Integer winding numbers · Kosterlitz-Thouless transition
Grid size:
40
Temperature T/J:
0.89
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Vorticity
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Vortex count (+)
—
Antivortex count (−)
—
Total charge
—
MC sweeps
0
XY model:
H = −J Σᵢⱼ cos(θᵢ−θⱼ)
Each spin has angle θ ∈ [0,2π).
Vortex:
winding number = ±1 around a plaquette. Topologically protected — cannot be removed locally.
KT transition
(T_KT ≈ 0.89 J): vortex–antivortex pairs unbind, driving a BKT phase transition — no broken symmetry but topological order.