Localization in disordered systems with interactions

We present an improved numerical approach to the study of disorder and interactions in quasi-1D systems which combines aspects of the transfer matrix method and the density matrix renormalization group which have been successfully applied to disorder and interacting problems respectively. The method is applied to spinless fermions in 1D and a generalization to finite cross-sections is outlined.      

Multifractality and scaling in disordered mesoscopic systems

We suggest a new method for investigating scaling properties of mesoscopic observables and their distributions in disordered systems showing metal-insulator transition. In such systems quantum interference effects lead to multifractal structure of eigenstates on scales much smaller than the correlation length of the transition which can be described by a set of exponents, thef() spectrum. The analysis off() spectra can be extended to any scaling variable. Multifractality is an indication for broad distributions of these variables. If the transition is governed by one correlation length only then thef() spectra of normalized scaling variables must be universal. The critical exponentv of the correlation length is determined by the value (0) wheref() takes its maximum and the scaling exponent of normalizationxv ^–1=(0)+x. As an illustrative example we calculate numerically thef() spectra of eigenstates in the critical regime of 2d disordered electron systems in high magnetic fields. We find similarf() spectra indicating universal log-normal distributions of scaling variables.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Magnetic phase transitions in amorphous systems with competing exchange interactions

A method is proposed for analyzing magnetic phase transitions within the Ising model under the conditions of competing direct and indirect exchange interactions. It is demonstrated that the competition of exchange interactions leads to a reentrant phase transition between the ferromagnet and spin glass near the percolation threshold below the Curie temperature.     

Domain growth and aging scaling in coarsening disordered systems

We explore the electronic and transport properties out of a biased multilayer hexagonal boron nitride (h-BN) by first-principles calculations. The band gaps of multilayer h-BN decrease almost linearly with increasing perpendicular electric field, irrespective of the layer number N and stacking manner. The critical electric filed (E ₀) required to close the band gap decreases with the increasing N and can be approximated by E ₀ = 3.2 / (N ? 1) (eV). We provide a quantum transport simulation of a dual-gated 4-layer h-BN with graphene electrodes. The transmission gap in this device can be effectively reduced by double gates, and a high on-off ratio of 3000 is obtained with relatively low voltage. This renders biased MLh-BN a promising channel in field effect transistor fabrication.     

Absence of spontaneous magnetization in spin systems with competing interactions

It is rigorously proved that spontaneous magnetization is absent in disordered spin systems if the strength of interaction is distributed symmetrically around a vanishing mean value, as a consequence of local gauge symmetry. This result is extended also to asymmetric distributions. A comment is made on gauge symmetry and frustration in quantum spin systems.     

Corrections to scaling for period doubling

We have studied a multiple scaling which describes corrections to scaling. For the period doubling in one-dimensional dissipative maps, two-dimensional areapreserving maps, and four-dimensional symplectic maps, the multiple scaling is seen to be well-obeyed, and new scaling factors have been found. The multiple scaling is also seen to be a very powerful tool for searching for scaling behavior.     

Corrections to scaling for branched polymers

We extend exact series enumerations for the mean square radius of gyration for lattice animals up to sizeN=19 on the square andN=12 on the simple cubic lattices. We have reanalysized the corrections to scaling exponents using the new data and found =0.5±0.05 and =0.45±0.1 in 2 and 3 dimensions respectively.     

Corrections to scaling for diffusion exponents on three-dimensional percolation systems at criticality

Recent results of Monte Carlo simulations of the ant-in-the-labyrinth method in three-dimensional percolation lattices are reanalyzed in the light of more accurate corrections to scaling ansatz, motivated by inconsistent results that have appeared in the literature. The results are observed to be sensitive to the form of the scaling correction terms. Using a single correction term, we estimate the valuek=0.197±0.004 for the anomalous diffusion exponent at criticality. When two correction terms are included,k=0.200±0.002 is obtained. These new estimates are consistent with known theoretical bounds, with recent series expansion results, and with numerical calculations of the conductance of random resistor networks above criticality.     

Hubert model for modulated states in systems with competing exchange interactions

Within a continuum model for magnetic systems with competing interactions introduced by Hubert the classification of all possible modulated structures for axial easy-plane systems has been carried out, and the phase portraits for these solutions are constructed. Analytic solutions for the structure of isolated domain walls between helicoids of different chirality are presented. The equilibrium structures of the modulated phases in an applied magnetic field and the critical field for transitions from helical to fan phase are in qualitative agreement with results obtained within the corresponding discretized model and various experimental data.     

Corrections to scaling and finite size effects

Numerical investigations of critical phenomena might lead to different leading correction-to-scaling terms, depending on the type of analysis. We discuss which leading correction-to-scaling behavior is expected for finite system sizes, using two-dimensional percolation as our main example. It turns out that a finite-size scaling from length L to L - 1 is less perturbed by correction-to-scaling terms.     

Dipole-dipole interactions of high-spin paramagnetic centers in disordered systems

Dipole-dipole interactions between distant paramagnetic centers (PCs) where at least one PC has spinS>1/2 are examined. The results provide a basis for the application of pulsed electron-electron double resonance method to the measurement of distances between PCs involving high-spin species. A projection operator technique based on spectral decomposition of the secular Hamiltonian is used to calculate electron paramagnetic resonance (EPR) line splitting caused by the dipole coupling. This allows calculation of operators projecting an arbitrary wave function onto high-spin PC eigenstates when the eigenvectors of the Hamiltonian are not known. The effective spin vectors — that is, the expectation values for vector spin operators in the PC eigenstates — are calculated. The dependence of these effective spin vectors on the external magnetic field is calculated. There is a qualitative difference between pairs having at least one integer spin (non-Kramers PC) and pairs of two half-integer (Kramers PC) spins. With the help of these effective spin vectors, the dipolar line shape of EPR lines is calculated. Analytical relations are obtained for PCs with spinS=1/2 and 1. The dependence of Pake patterns on variations of zero-field splitting, Zeeman energy, temperature and dipolar coupling are illustrated.     

Atomic dynamics in liquids with competing interactions

The influence of the type of atomic interaction on the atomic dynamics is studied for liquid Na(x)Sn(1-x) (x = 0.9, 0.77, 0.57, 0.5, 0.33) alloys by cold neutron inelastic scattering. The dispersions obtained from the longitudinal current correlation function J(l)(Q,omega) show clear evidence for the dependence of the dynamics on the type of interaction (metallic, ionic, partly covalent) tuned by changing the composition of the alloy. For the first time, a second dispersion branch is observed in the total J(l)(Q,omega) around Q(p), the position of the principal peak of S(Q), for the Sn-rich compositions. The dynamic properties are discussed and compared to results of recent ab initio molecular dynamics simulations.     

Corrections to cluster-radius scaling for branched polymers and percolation

We report analyses of series enumerations for the mean radius of gyration for isotropic and directed lattice animals and for percolation clusters, in two and three dimensions. We allow for the leading correction to the scaling behaviour and obtain estimates of the leading correction-to-scaling exponent . We find -0.640±0.004 and =0.87±0.07 for isotropic animals in 2d, and =0.64±0.06 in 3d. For directed lattice animals we argue that the leading correction has= or= ; we also estimate =0.82±0.01 and 0.69 ±0.01 ind=2, 3 respectively. For percolation clusters at and abovep _c, we find (p _c) =0.58±0.06 and (p>p _c)=0.84±0.09 in 2d, and (p _c)=0.42±0.11 and (p>p _c)=0.41 ±0.09 in 3d.