Continuous-Mixture Autoregressive Networks Learning the Kosterlitz-Thouless Transition

The Kosterlitz-Thouless Transition

Matter in the universe is organised in a hierarchical structure. At the bottom we have elementary particles: quarks, gluons, electrons etc. At present we don’t know what these particles 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 of molecules. Atoms and molecules gives us gas, li...

The Kosterlitz-Thouless Phase Transition

Introduction to the Berezinskii-Kosterlitz-Thouless Transition

This essay examines the Berezinskii-Kosterlitz-Thousless transition in the two-dimensional XY model. It is an imporant example of phase transitions occuring without an ordered phase or symmetry breaking, and introduced topological ideas into the concerns of condensed matter physicists.

Resistance scaling at the Kosterlitz-Thouless transition.

We study the linear resistance at the Kosterlitz–Thouless transition by Monte Carlo simulation of vortex dynamics. Finite size scaling analysis of our data show excellent agreement with scaling properties of the Kosterlitz–Thouless transition. We also compare our results for the linear resistance with experiments. By adjusting the vortex chemical potential to an optimum value, the resistance at...

Surface properties at the Kosterlitz-Thouless transition

Monte Carlo simulations of the two-dimensional XY model are performed in a square geometry with free and mixed fixed-free boundary conditions. Using a Schwarz-Christoffel conformal mapping, we deduce the exponent η of the order parameter correlation function and its surface equivalent η‖ at the Kosterlitz-Thouless transition temperature. The well known value η(TKT) = 1/4 is easily recovered eve...