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Variance of the Topological Charge as an Order Parameter for the KT Model

Norouzi, Hossein | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52182 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rouhani, Shahin
  7. Abstract:
  8. XY Model due to topological defects (or vortex) has topological phase transition. According Kosterlitz-Thouless (KT) theory, phase transition is from low-temperature bounded vortices to high-temperature free vortices. XY model is appropriate choice for description of superfluidity in 2d thin films of . KT theory predicts universal jump in mass density of 2d superfluid in phase transition point. It is confirmed experimentally by Bishop and Reppy. All critical behavior of XY model is described with 2d coulomb gas, vortices are topological charges of the gas. KT predict variance of topological charge should obey of the “surface law vs perimeter law”, similar to behavior of Wilson loop in lattice gauge theory. Contrary to this prediction, Dhar prove this quantity in all temperatures is proportional to perimeter. Despite the above disagreements, we will show this quantity is order parameter of XY model. Of course, since phase transition in XY model is not accompanied by symmetry breaking then order parameter do not reflects symmetry of system, phase transition occur only when characteristic behavior of order parameter changes. For experimental observation of order parameter we use from the hyperuniformity. The results of hyperuniformity are compared with KT and Dhar arguments
  9. Keywords:
  10. Kosterlitz-Thouless (KT) Theory ; Topological Phase Transition ; Topological Charge ; Two Dimentional Coulomb Gas ; Order Parameter ; Hyperuniformity ; Structure Factor

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