XY MODEL — KOSTERLITZ-THOULESS TRANSITION

2D XY Model · Vortex Unbinding · Topological Phase Transition

PARAMETERS

T_KT ≈ 0.898 J (exact)

ORDER PARAMETERS

T/T_KT: 0.89
Phase: ORDERED
Helicity Υ: 0.000
Free vortices: 0
Bound pairs: 0
■ Vortex (+1)
■ Antivortex (-1)

KT CURVE

Helicity modulus vs T

ABOUT

KT transition (1973 Nobel 2016): topological phase transition mediated by vortex-antivortex unbinding. Below T_KT: bound pairs, algebraic order, power-law correlations. Above: free vortices proliferate, exponential decay. No conventional order parameter — topological!
Spin arrows colored by angle · + vortices red, − antivortices blue