Transcription of The Kosterlitz-Thouless Transition
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The Kosterlitz-Thouless Transition
The Kosterlitz-Thouless TransitionHenrik Jeldtoft JensenDepartment of MathamticsImperial CollegeKeywords: Generalised rigidity, Topological defects, Two DimensionalXY-model, Superconductivity, Two dimensional Melting, Renormalization1 IntroductionMatter in the universe is organised in a hierarchical structure. At the bottom we haveelementary particles: quarks, gluons, electrons etc. At present we don t know what theseparticles are made off. But we believe we know that quarks, gluons etc. make up protons,neutrons, etc. These then go together to make atoms, that are the building blocks ofmolecules. Atoms and molecules gives us gas, liquids and solids from which we get starsand planets which are grouped together in galaxies, that then form clusters and eventuallywe arrive at the entire universe.
1 2 Z dr 1 Z dr 2 sw(r 1) 2H (r 1) (r 2) sw(r 2))g: (4) The eld con gurations corresponding to local minima of Hare solutions to the extremal condition H (r) = 0 )r2 (r) = 0: (5) There are two types of solutions to this equation. The rst consists of the ground state (r) = constant. The second type of solutions consist of vortices in the ...
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