Spin-Level Hybridization between Ising and XY Models: A Monte Carlo Study

Hans A. De Raedt, Bart De Raedt, Jan Fivez +1 more

Hans A. De Raedt, Bart De Raedt, Jan Fivez +1 more

Anderson Barbosa Lima

Using Monte Carlo and spin dynamics techniques we have investigated the critical behavior of the classical fully frustrated XY and fully frustrated Planar Rotor models in two dimensions in square lattices of size up to 256. We have found that the models have two transitions a Berezinskii-Kosterliz-Thouless transition at TBKT = 0:3655(5) and an Ising transition at TI = 0:3690(3) for the fully frustrated XY model and a Berezinskii-Kosterliz-Thouless transition at TBKT = 0:4410(5) and an Ising transition at TI = 0:4505(5) for the fully frustrated Planar Rotor model. After this _rst step we have simulated the Z2 (Ising) transition in both fully frustrated Planar Rotator and fully frustrated XY models. We have shown that they can be understood as a percolation problem if we de_ne properly the connectivity of the system. The critical exponent of the mean cluster size, is found as = 2:2(2) close to the two dimensional Ising case, = 2:389. The critical Fisher's exponent is obtained as _ = 1:8(1), close to the two dimensional Ising value _ = 2:055. Also, weobtain the critical Z2 temperatures for both models using the percolation criterion which agree very well with other calculations.Some preliminary calculations was done in the XY model in order to obtain the neutron scattering correlation function S(q; !) and the dispersion relation.

Walter Selke

Richard C. Brower, N. A. Gross, Kevin J. M. Moriarty

We present an overview of the new methods for embedding Ising spins in continuous fields to achieve accelerated cluster Monte Carlo algorithms. The methods of Brower and Tamayo and Wolff are summarized and variations are suggested for the O(N) models based on multiple embedded Z2 spin components and/or correlated projections. Topological features are discussed for the XY model and numerical simulations presented for d=2, d=3 and mean field theory lattices.

Misha Gofman, Joan Adler, Amnon Aharony A +2 more