Kosterlitz-Thouless transition

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The Kosterlitz-Thouless transition (also known as the Berezinskii-Kosterlitz-Thouless (BKT) phase transition)[1] [2] [3] [4] 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 [4]):

T_c = \frac{\pi J}{k_B}

where J is the spin-spin coupling constant. This can be obtained as (Eq.58 in [4]):

\frac{\pi J}{k_BT_c}-1 \approx \pi \tilde{y}_c(0) \exp\left(\frac{-\pi^2J}{k_BT_c} \right) \approx 0.12

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