KOSTERLITZ-THOULESS TRANSITION

Topological Defect Unbinding & 2D XY Model
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The Kosterlitz-Thouless (KT) transition (Nobel 2016) is a topological phase transition in 2D XY models — no symmetry breaking, but a change in quasi-long-range order. Below T_KT ≈ 0.89J/k_B, vortex-antivortex pairs are bound; above T_KT, they unbind and proliferate, destroying algebraic order. Left: spin field (arrows). Right: vortex (+1) and antivortex (-1) positions detected by plaquette winding.