Kosterlitz-Thouless transition

The Kosterlitz-Thouless transition is a special transition seen in the the XY model for interacting spin systems. The XY model is a 2-Dimensional vector spin model that posseses U(1) or circular symmetry.This system is not expected to possess a normal Second order Phase transition. This is because the expected ordered phase of the system is destroyed by transverse fluctuations,i.e the Goldstone modes(see Goldstone boson) associated with this broken continuous symmetry,which logarithmically diverge with system size. This is a specific case of what is called the Mermin Wagner theorem in spin systems.

KT Transition : Disordered Phases with different correlations

In the XY model in two dimensions,a second order phase transition is not seen. However,one finds a low temperature disordered phase with a power law correlation(see Correlation function (statistical mechanics)),with a temperature dependent power. The transition from the High temperature disordered phase with the exponential correlation to this low temperature disordered phase with a power law correlation is what is the Kosterlitz thouless transition.

Role of Vortices

In the XY model in 2 dimensions,vortices are topologically stable configurations. It is found that the high temperature disordered phase with exponential correlation is a result of the formation of vortices. The temperature at which the KT transition occurs is in fact that at which vortex generation becomes thermodynamically favourable. At temperatures below this,the system has a power law correlation.

See also

• Goldstone boson
• Ising model
• Potts model
• Topological defect

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