Talk: The Berezinskii-Kosterlitz-Thouless transition in a mobile XY model

The Berezinskii-Kosterlitz-Thouless phase transition (KT-transition) is subject to scientific research since the early 70s. Unlike many phase transitions, the KT-transition [1] does not feature the breaking of a continuous symmetry at the critical temperature,instead the transition manifests itself in the proliferation of topological defects. A very prominent model to study the KT-transition and its characteristics is the classical XY-model with planar rotors, usually fixed on the nodes of a lattice. Here we show the occurrence of the KT-transition and system characteristics around the transition temperature in a mobile system with translational degrees of freedom. For comparative purposes, we also investigate the classical XY-model on a trigonal grid. Besides an analysis of the topological defects, our main tool to pin down the transition is spin-correlations. We find that both systems undergo the transition predicted by Kosterlitz, from a quasi-long-range decay in spatial spin-correlations to an exponential decay , being the distance between two spins. These we use to calculate critical exponents (Fig. 1, left) that fit well with the predictions of Kosterlitz [1]. Similar results we find for dynamic spin-correlations and their respective critical exponents (Fig. 1, right).


Fig. 1: Critical exponents of the mobile XY-model from spatial correlations (left) and dynamic correlations (right). Simulation data in green, fits to predictions of Kosterlitz for as dashed line, fits for as drawn-through line. Arbitrary temperature units.

References:
[1] J.M. Kosterlitz, Journal of Physics C: Solid State Physics, 7(6), 1046, (1974)