Kosterlitz-Thouless transition

The Kosterlitz – Thouless transition , also known as the Berezinsky – Kosterlitz – Thouless transition , according to John M. Kosterlitz , David J. Thouless and Wadim Lwowitsch Beresinski , is a special type of phase transition with an exponentially diverging correlation length at the critical point . It is a two-dimensional effect and has been observed in thin films of liquid helium and superconductors as well as in Bose-Einstein condensates . Historically, it is the first example of a topological phase transition. Kosterlitz and Thouless received the Nobel Prize in Physics for this in 2016 .

Phase transition

The Kosterlitz-Thouless transition can be observed in the two-dimensional XY model , a simple spin model with nearest-neighbor interaction. This system takes place in two dimensions not the usual second-order phase transition after Ehrenfest classification , as the parent phase in this dimension by transverse , logarithmically diverging with the system-scale fluctuations  ( Goldstone modes is destroyed) (an example of Mermin-Wagner Theorems ). Instead, the correlation length diverges exponentially in the form of the Kosterlitz-Thouless transition

${\displaystyle \xi (T)\sim \exp \left(\mathrm {const} \cdot {\sqrt {\frac {T_{C}}{T-T_{C}}}}\right)}$

for with ${\displaystyle T>T_{C}}$

• Correlation length ${\displaystyle \xi }$
• absolute temperature ${\displaystyle T}$
• critical temperature ${\displaystyle T_{C}.}$

The KT transition is a phase transition of infinitely high order.

The phase transition can be understood as the transition from bound vortex-anti-vortex states below the critical temperature (vortices are topologically stable excitations in the XY model) to unbound vortex states.

literature

• VL Berezinskii: Destruction of Long-range Order in One-dimensional and Two-dimensional Systems having a Continuous Symmetry Group I. Classical Systems , Sov. Phys. JETP 32, 493 (1971), pdf
• JM Kosterlitz, DJ Thouless, Ordering, metastability and phase transitions in two-dimensional systems , J. Phys. C 6: Solid State Phys., 1181 (1973)
• JM Kosterlitz: Critical exponents of the two dimensional XY model , J. Phys. C 7, 1046 (1974)
• BI Halperin , DR Nelson : Theory of two dimensional melting , Phys. Rev. Lett. 41: 121 (1978) abstract
• AP Young: Melting and the vector Coulomb gas in two dimensions , Phys. Rev. B 19, 1855 (1979)
• JV José, 40 Years of Berezinskii – Kosterlitz – Thouless Theory , World Scientific , 2013, ISBN 978-981-4417-65-5