Kosterlitz-Thouless transition

The Kosterlitz-Thouless transition (also known as the Berezinskii-Kosterlitz-Thouless (BKT) phase transition) is a phase transition found in the two-dimensional XY model. Below the transition temperature, $T_{KT}$, the system plays host to a 'liquid' of vortex-antivortex pairs that have zero total vorticity. Above $T_{KT}$ these pairs break up into a gas of independent vortices.

For the XY model the critical temperature is given by (Eq.4 in ):

$T_{c}={\frac {\pi J}{k_{B}}}$

where $J$ is the spin-spin coupling constant. This can be obtained as (Eq.58 in ):

${\frac {\pi J}{k_{B}T_{c}}}-1\approx \pi {\tilde {y}}_{c}(0)\exp \left({\frac {-\pi ^{2}J}{k_{B}T_{c}}}\right)\approx 0.12$

See also

• XY universality class

References

Related reading

• B. I. Halperin and David R. Nelson "Theory of Two-Dimensional Melting", Physical Review Letters 41 pp. 121-124 (1978)
• A. P. Young "Melting and the vector Coulomb gas in two dimensions", Physical Review B 19 pp. 1855-1866 (1979)
• David R. Nelson and B. I. Halperin "Dislocation-mediated melting in two dimensions", Physical Review B 19 pp. 2457-2484 (1979)
• Farid F. Abraham "Melting in Two Dimensions is First Order: An Isothermal-Isobaric Monte Carlo Study", Physical Review Letters 44 pp. 463-466 (1980)
• Farid F. Abraham "Two-dimensional melting, solid-state stability, and the Kosterlitz-Thouless-Feynman criterion", Physical Review B 23 pp. 6145-6148 (1981)
• Katherine J. Strandburg "Two-dimensional melting", Reviews of Modern Physics 60 pp. 161-207 (1988)
• Hagen Kleinert Gauge Fields in Condensed Matter, Vol. I, " SUPERFLOW AND VORTEX LINES", pp. 1–742, Vol. II, "STRESSES AND DEFECTS", pp. 743–1456, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0 (also available online: Vol. I and Vol. II)
• Kurt Binder, Surajit Sengupta and Peter Nielaba "The liquid-solid transition of hard discs: first-order transition or Kosterlitz-Thouless-Halperin-Nelson-Young scenario?", Journal of Physics: Condensed Matter 14 pp. 2323-2333 (2002)
• "40 Years of Berezinskii–Kosterlitz–Thouless Theory" (Ed. Jorge V José) World Scientific Publishing (2013) ISBN 978-981-4417-63-1
• Nobel Prize in Physics 2016 'Scientific Background'