Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts.pdfVIP

Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts N. Akino1 and J.M. Kosterlitz2 1Institut f¨ur Physik, WA 331, Johannes Gutenberg-Universit¨at, D-55099 Mainz, Germany and 2 2Department of Physics, Brown University, Box 1843, Providence, RI 02912, USA 0 0 (Dated: February 6, 2008) 2 The XY model with quenched random disorder is studied by a zero temperature domain wall r renormalization group method in 2D and 3D. Instead of the usual phase representation we use the a charge (vortex) representation to compute the domain wall, or defect, energy. For the gauge glass M corresponding to the maximum disorder we reconfirm earlier predictions that there is no ordered phase in 2D but an ordered phase can exist in 3D at low temperature. However, our simulations 4 yield spin stiffness exponents θs ≈ −0.36 in 2D and θs ≈ +0.31 in 3D, which are considerably 1 larger than previous estimates and strongly suggest that the lower critical dimension is less than three. For the ±J XY spin glass in 3D, we obtain a spin stiffness exponent θs ≈ +0.10 which ] h supports the existence of spin glass order at finite temperature in contrast with previous estimates c which obtain θs 0. Our method also allows us to study renormalization group flows of both the e coupling constant and the disorder strength with length scale L. Our results