The phase diagram of 2D polar condensates in a magnetic field

Spin one condensates in the polar (antiferromagnetic) phase in two dimensions are shown to undergo a transition of the Ising type, in addition to the expected Kosterlitz--Thouless (KT) transition of half vortices, due to the quadratic Zeeman effect. We establish the phase diagram in terms of temperature and the strength of the Zeeman effect using Monte Carlo simulations. When the Zeeman effect is sufficiently strong the Ising and KT transitions merge. For very strong Zeeman field the remaining transition is of the familiar integer KT type.Comment: 4 pages, 7 figure

Superconducting phase transitions in frustrated Josephson-junction arrays on a dice lattice

Transport measurements are carried out on dice Josephson-junction arrays with the frustration index $f=1/3$ and 1/2 which possess, within the limit of the $XY$ model, an accidental degeneracy of the ground states as a consequence of the formation of zero-energy domain walls. The measurements demonstrate that both the systems undergo a phase transition to a superconducting vortex-ordered state at considerably high temperatures. The experimental findings are in apparent contradiction with the theoretical expectation that frustration effects in the $f=1/3$ system are particularly strong enough to suppress a vortex-ordering transition down to near zero temperature. The data for $f=1/2$ are more consistent with theoretical evaluations. The agreement between the experiments and the Monte Carlo simulations of a $XY$ model for $f=1/3$ suggests that the order-from-disorder mechanism for the removal of an accidental degeneracy may still be effective in the $f=1/3$ system. The transport data also reveal that the dice arrays with zero-energy domain walls experience a much slower critical relaxation than other frustrated arrays only with finite-energy walls.Comment: 4 pages, 4 figure

Comment on "Probing vortex unbinding via dipole fluctuations"

We demonstrate that the method suggested by Fertig and Straley [Phys. Rev. B 66, 201402 (2002)] for the identification of different phases in two-dimensional XY models does not allow to make any unambiguous conclusions and make a tentative proposal of another approach to this problem.Comment: The final version - as published in Physical Review B (2 pages). Two paragraphs have been added with a proposal of a new approach to distinguishing phases with bound and unbound vortice

A cluster algorithm for resistively shunted Josephson junctions

We present a cluster algorithm for resistively shunted Josephson junctions and similar physical systems, which dramatically improves sampling efficiency. The algorithm combines local updates in Fourier space with rejection-free cluster updates which exploit the symmetries of the Josephson coupling energy. As an application, we consider the localization transition of a single junction at intermediate Josephson coupling and determine the temperature dependence of the zero bias resistance as a function of dissipation strength.Comment: 4 page