CRITICAL PROPERTIES OF DISORDERED SYSTEMS

We analyzed the localization transition of hardcore bosons with random site energies in mean field theory. It had often been asserted that no such transition could occur, because the perfect connectivity of the mean field lattice enabled particles to move between sites with similar energies without passing through intermediate states which were not in resonance. We showed that this statement was not true, and that with an appropriate choice of site energy distribution a localization transition can occur. We characterized this transition using the inverse participation ratio, the single site Green's function, the superfluid order parameter and the corresponding susceptibility, determining the appropriate exponents.

We developed a theory for the quantum gauge glass, by considering disorder in both the off diagonal (hopping) terms and the site energies. This model is closely related to XY magnets and bosons in random media. Materials which are realizations of such spin-glass models include the LiHoYF compounds. A crucial unresolved issue has been to explain the behavior of the non-linear susceptibility which does not diverge experimentally, but was found to diverge in recent theoretical studies. We calculated the phase diagram which consists of a superfluid phase, and Weak and Strong Glass regions. Strikingly, at the Strong Glass transition the non-linear susceptibility does not diverge.

We have also revisited an old problem concerning the relation between critical exponents in disordered classical systems. We showed that the often quoted ``Chayes inequality'' is, in fact, generated only by the procedure used to do the disorder averaging, and different procedures give quite different exponent bounds. This work attracted considerable interest as it challenged a commonly held truth in critical phenomena. We also introduced a new procedure to analyze the shifts in critical points on finite lattices.

Finally, the study of disordered Hubbard models and the possibility of a two-dimensional metal-insulator transition has been of interest to us. We showed that the on-site U in the Hubbard Hamiltonian can change the qualitative temperature dependence of the conductivity from insulating to metallic. Relevant Publications:

[61.] F. Pazmandi, G.T. Zimanyi and R.T. Scalettar,
``Mean-field Theory of the Localization Transition,''
Phys. Rev. Lett. 75, 1356 (1995).

[65.] F. Pazmandi, G.T. Zimanyi and R.T. Scalettar,
``Mean-Field Theory for Quantum Gauge Glasses,''
Europhys. Lett. 38, 255 (1997).

[79.] F. Pazmandi, R.T. Scalettar and G.T. Zimanyi,
``Revisiting the Theory of Finite Size Scaling in Disordered Systems: nu Can Be Less Than 2/d,''
Phys. Rev. Lett. 79, 5130 (1997).

[80.] C. Huscroft and R.T. Scalettar,
``Evolution of the Density of States Gap in a Disordered Superconductor",
Phys. Rev. Lett. 81, 2775 (1998).

[84.] M. Ulmke, P. J. H. Denteneer, V. Janis, R. T. Scalettar, A. Singh, D. Vollhardt, and G. T. Zimanyi,
``Disorder and Impurities in Hubbard Antiferromagnets", Advances in Solid State Physics, 38, 369 (1999).

[86.] R.T. Scalettar, N. Trivedi, C. Huscroft, and M. Randeria,
``Quantum Monte Carlo Study of the Disordered, Attractive Hubbard Model",
Phys. Rev. B59, 4364 (1999).

[92.] P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi,
``Conducting phase in the two-dimensional disordered Hubbard model",
Phys. Rev. Lett. 83, 4610 (1999).

[108.] P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi,
``Particle-Hole Symmetry and the Effect of Disorder on the Mott--Hubbard Insulator,''
Phys. Rev. Lett. 87, 6401 (2001).

[125.] P.J.H. Denteneer and R.T. Scalettar,
"Interacting electrons in a two-dimensional disordered environment: Effect of a Zeeman magnetic field,''
Phys. Rev. Lett. 90, 246401 (2003).

[138.] N. Trivedi, P.J.H. Denteneer, D. Heidarian, and R.T. Scalettar,
"Effect of Interactions, Disorder and Magnetic Field in the 2D Hubbard Model,''
Pramana-J. of Physics 64, 1051 (2005).

[147.] Daniel Hurt, Evan Odabashian, Warren Pickett, Richard Scalettar, Felipe Mondaini, Thereza Paiva, and Raimundo dos Santos,
"Destruction of Superconductivity by Impurities in the Attractive Hubbard Model",
Phys. Rev. B72, 144513 (2005).

[148.] K. Aryanpour, R.T. Scalettar, W.E. Pickett, T.C. de Lacerda Paiva, M. Mayr, and E. Dagotto,
"Effect of Inhomogeneity on s-wave Superconductivity in the Attractive Hubbard Model",
Phys. Rev. B73, 104518 (2006).

[151.] C.M. Chaves, T. Paiva, J. d'Albuquerque e Castro, F. Hebert, R.T. Scalettar, G.G. Batrouni, and B. Koiller,
"The magnetic susceptibility of exchange-disordered antiferromagnetic finite chains",
Phys. Rev. B73, 104410 (2006).

[61.] F. Pazmandi, G.T. Zimanyi and R.T. Scalettar, ``Mean-field Theory of the Localization Transition,'' Phys. Rev. Lett. 75, 1356 (1995).
[65.] F. Pazmandi, G.T. Zimanyi and R.T. Scalettar, ``Mean-Field Theory for Quantum Gauge Glasses,'' Europhys. Lett. 38, 255 (1997).
[79.] F. Pazmandi, R.T. Scalettar and G.T. Zimanyi, ``Revisiting the Theory of Finite Size Scaling in Disordered Systems: nu Can Be Less Than 2/d,'' Phys. Rev. Lett. 79, 5130 (1997).
[80.] C. Huscroft and R.T. Scalettar, ``Evolution of the Density of States Gap in a Disordered Superconductor", Phys. Rev. Lett. 81, 2775 (1998).
[84.] M. Ulmke, P. J. H. Denteneer, V. Janis, R. T. Scalettar, A. Singh, D. Vollhardt, and G. T. Zimanyi, ``Disorder and Impurities in Hubbard Antiferromagnets", Advances in Solid State Physics, 38, 369 (1999).
[86.] R.T. Scalettar, N. Trivedi, C. Huscroft, and M. Randeria, ``Quantum Monte Carlo Study of the Disordered, Attractive Hubbard Model", Phys. Rev. B59, 4364 (1999).
[92.] P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi, ``Conducting phase in the two-dimensional disordered Hubbard model", Phys. Rev. Lett. 83, 4610 (1999).
[108.] P.J.H. Denteneer, R.T. Scalettar, and N. Trivedi, ``Particle-Hole Symmetry and the Effect of Disorder on the Mott--Hubbard Insulator,'' Phys. Rev. Lett. 87, 6401 (2001).
[125.] P.J.H. Denteneer and R.T. Scalettar, "Interacting electrons in a two-dimensional disordered environment: Effect of a Zeeman magnetic field,'' Phys. Rev. Lett. 90, 246401 (2003).
[138.] N. Trivedi, P.J.H. Denteneer, D. Heidarian, and R.T. Scalettar, "Effect of Interactions, Disorder and Magnetic Field in the 2D Hubbard Model,'' Pramana-J. of Physics 64, 1051 (2005).
[147.] Daniel Hurt, Evan Odabashian, Warren Pickett, Richard Scalettar, Felipe Mondaini, Thereza Paiva, and Raimundo dos Santos, "Destruction of Superconductivity by Impurities in the Attractive Hubbard Model", Phys. Rev. B72, 144513 (2005).
[148.] K. Aryanpour, R.T. Scalettar, W.E. Pickett, T.C. de Lacerda Paiva, M. Mayr, and E. Dagotto, "Effect of Inhomogeneity on s-wave Superconductivity in the Attractive Hubbard Model", Phys. Rev. B73, 104518 (2006).
[151.] C.M. Chaves, T. Paiva, J. d'Albuquerque e Castro, F. Hebert, R.T. Scalettar, G.G. Batrouni, and B. Koiller, "The magnetic susceptibility of exchange-disordered antiferromagnetic finite chains", Phys. Rev. B73, 104410 (2006).