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Aiming at the study of critical phenomena in the presence of boundaries with a non-trivial shape we discuss how lattices with an adaptive lattice spacing can be implemented. Since the parameters of the Hamiltonian transform non-trivially…
We find that competition between random Kondo and random magnetic correlations results in a quantum phase transition from a local Fermi liquid to a spin liquid. The local charge susceptibility turns out to have exactly the same critical…
We investigate the impact of non-local perturbations on driven diffusive systems. Two different problems are considered here. In one case, we introduce a non-local particle conservation along the direction of the drive and in another case,…
Momentum-dependent excitation spectra of the two-dimensional Hubbard model on the square lattice have been investigated at zero temperature on the basis of the full self-consistent projection operator method in order to clarify nonlocal…
Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that…
For $n\in [-2,2]$ the $O(n)$ model on a random lattice has critical points to which a scaling behaviour characteristic of 2D gravity interacting with conformal matter fields with $c\in [-\infty,1]$ can be associated. Previously we have…
We study the effect of coherent propagation of two interacting particles in a disordered potential. The dependence of the enhancement factor for coherent localization length due to interaction is investigated numerically in the model of…
In this paper I introduce the probability distribution of the local overlap in spin glasses. The properties of the local overlaps are studied in details. These quantities are related to the recently proposed local version of the fluctuation…
We consider the effect of droplet excitations in the random first order transition theory of glasses on the configurational entropy. The contribution of these excitations is estimated both at and above the ideal glass transition…
We discuss the mechanism and the conditions for the appearance of synchronized charge oscillations which have been observed experimentally and theoretically after strong photoexcitation of dimerized systems. In the Hubbard model with…
We present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions. By generalizing our previous work, we combine duality and gauge symmetry for replicated random systems…
The dissipative XY model in two spatial dimensions belongs to a new universality class of quantum critical phenomena with the remarkable property of the decoupling of the critical fluctuations in space and time. We have shown earlier that…
We study a directed coupled map lattice model in two dimensions, with two degrees of freedom associated with each lattice site. The two freedoms are coupled at a fraction $c$ of lattice bonds acting as quenched random defects. In the case…
In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrodinger equation model, to the case of two-component…
We investigate the unjamming response of disordered packings of frictional hard disks with the help of computer simulations. First, we generate jammed configurations of the disks and then force them to move again by local perturbations. We…
We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that…
The effect of weak localization on spin relaxation in a two-dimensional system with a spin-split spectrum is considered. It is shown that the spin relaxation slows down due to the interference of electron waves moving along closed paths in…
We study the propagation of a density perturbation in a weakly interacting boson gas confined on a lattice and in the presence of square dimerized impurities. Such a two-dimensional random-dimer model (2D-DRDM), previously introduced in…
It is well known that for ordinary one-dimensional (1D) disordered systems, the Anderson localization length $\xi$ diverges as $\lambda^m$ in the long wavelength limit ($\lambda\rightarrow \infty$ ) with a universal exponent $m=2$,…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…