1. Zero Field Superconducting Transition with Columnar Defects A. Vestergren, Mats WallinS. TeitelHans Weber KTH, StockholmUniver. RochesterLuleå Univer. Why is this interesting? When B = 0, adding point disorder does not change the critical behavior of the superconducting transition. However the Harris criteria suggests that columnar disorder will. Measurement of new critical exponents would provide precision check on the validity of the 3D XY model as a model for critical behavior in superconductors. Applications to the T = 0 superconductor to insulator quantum phase transition in 2D thin films, and to the Mott transition for bosons in 2D optical lattices

2. 3D XY model represents kinetic energy of flowing supercurrents is phase of superconducting wave function at site i of a cubic grid of sites. There is no magnetic field. order parameter Binder ratio anisotropic critical scaling columnar disorder equally likely but with translational invariance along z direction

3. transverse correlation length longitudinal correlation length correlation length exponent anisotropy exponent Plot vs. L z for different fixed L at a given T. Let L z max be the maximizing L z Curves of for different L all intersect at t = 0.

4. curves intersect at T c = 2.05 scaling collapse of data determines = 1.2 at T c, determines = 1.3 consistency check universal curve at T c

5. As for disorder-free case, an exact duality transformation maps this columnar disordered XY model onto a model of short range interacting loops. Critical behavior must stay the same. Therefore the above values for critical exponents, computed for the XY model with long range interacting vortex loops,, remain the same for a screened model with short range interacting vortex loops, i.e. finite. Conclusions columnar disorder disorder-free system value of > 1 is consistent with requirements of Harris criterion for a stable disorder fixed point.

6. Comparison with other results Experiments on YBCO thin films by Koetzler and co-workers find, Compares to our value Simulations by Prokof’ev and Svistunov on dual 2D boson problem find,, roughly in agreement with our value. They could not compute. Ref: A. Vestergren, M. Wallin, S. Teitel and H. Weber Phys. Rev. B 70, 54508 (2004)