Spin and chiral stiffness of the XY spin glass in two dimensions

We analyze the zero-temperature behavior of the XY Edwards-Anderson spin glass model on a square lattice. A newly developed algorithm combining exact ground-state computations for Ising variables embedded into the planar spins with a specially tailored evolutionary method, resulting in the genetic embedded matching (GEM) approach, allows for the computation of numerically exact ground states for relatively large systems. This enables a thorough re-investigation of the long-standing questions of (i) extensive degeneracy of the ground state and (ii) a possible decoupling of spin and chiral degrees of freedom in such systems. The new algorithm together with appropriate choices for the considered sets of boundary conditions and finite-size scaling techniques allows for a consistent determination of the spin and chiral stiffness scaling exponents.Comment: 6 pages, 2 figures, proceedings of the HFM2006 conference, to appear in a special issue of J. Phys.: Condens. Matte

Origin of Spin Ice Behavior in Ising Pyrochlore Magnets with Long Range Dipole Interactions: an Insight from Mean-Field Theory

Recent experiments suggest that the Ising pyrochlore magnets ${\rm Ho_{2}Ti_{2}O_{7}}$ and ${\rm Dy_{2}Ti_{2}O_{7}}$ display qualitative properties of the ferromagnetic nearest neighbor spin ice model proposed by Harris {\it et al.}, Phys. Rev. Lett. {\bf 79}, 2554 (1997). The manifestation of spin ice behavior in these systems {\it despite} the energetic constraints introduced by the strength and the long range nature of dipole-dipole interactions, remains difficult to understand. We report here results from a mean field analysis that shed some light on the origin of spin ice behavior in (111) Ising pyrochlores. Specifically, we find that there exist a large frustrating effect of the dipolar interactions beyond the nearest neighbor, and that the degeneracy established by effective ferromagnetic nearest neighbor interactions is only very weakly lifted by the long range interactions. Such behavior only appears beyond a cut-off distance corresponding to $O(10^2)$ nearest neighbor. Our mean field analysis shows that truncation of dipolar interactions leads to spurious ordering phenomena that change with the truncation cut-off distance.Comment: 7 Color POSTSCRIPT figures included. To appear in Canadian Journal of Physics for the Proceedings of the {\it Highly Frustrated Magnetism 2000 Conference}, Waterloo, Ontario, Canada, June 11-15, 2000 Contact: [email protected]