Quasi-Long-Range Order and Vortex Lattice in the Three-State Potts Model

Overlap of two topological phases in the antiferromagnetic Potts model

By controlling the vortex core energy, the three-state ferromagnetic Potts model can exhibit two types of topological paradigms, including the quasi-long-range ordered phase and the vortex lattice phase [Phys. Rev. Lett. 116, 097206 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.097206]. Here, using Monte Carlo simulations using an efficient worm algorithm, we show that by controlling the vortex core energy, the antiferromagnetic Potts model can also exhibit the two topological phases, and, more interestingly, the two topological phases can overlap with each other.

Competing nematic interactions in a generalized XY model in two and three dimensions

We study a generalization of the XY model with an additional nematic-like term through extensive numerical simulations and finite-size techniques, both in two and three dimensions. While the original model favors local alignment, the extra term induces angles of 2π/q between neighboring spins. We focus here on the q=8 case (while presenting new results for other values of q as well) whose phase diagram is much richer than the well-known q=2 case. In particular, the model presents not only continuous, standard transitions between Berezinskii-Kosterlitz-Thouless (BKT) phases as in q=2, but also infinite-order transitions involving intermediate, competition-driven phases absent for q=2 and 3. Besides presenting multiple transitions, our results show that having vortices decoupling at a transition is not a sufficient condition for it to be of BKT type.