Topological Defects & Vortices
Click to place vortex defects — winding numbers classify them topologically
Create Defects
Winding number n:
+1
Field type:
XY spin
Nematic
Arrow density:
16
Relaxation:
ON
Clear All Defects
Add ±1 Pair
Total winding:
0
(topologically conserved)
n = (1/2π) ∮ ∇θ · dl
Vortex defects in 2D order parameter fields (XY magnets, superfluid, liquid crystals) are characterized by integer winding numbers.
n=+1
: source/vortex — arrows orbit CCW
n=-1
: antivortex — arrows orbit CW
n=½
: half-vortex in nematics (head-tail symmetry)
Kosterlitz-Thouless transition: vortex–antivortex pairs unbind at T_KT.