No Arabic abstract
The demagnetization curve, or initial magnetization curve, is studied by examining the embedded Barkhausen noise using the non-equilibrium, zero temperature random-field Ising model. The demagnetization curve is found to reflect the critical point seen as the systems disorder is changed. Critical scaling is found for avalanche sizes and the size and number of spanning avalanches. The critical exponents are derived from those related to the saturation loop and subloops. Finally, the behavior in the presence of long range demagnetizing fields is discussed. Results are presented for simulations of up to one million spins.
We discuss the application of wavelet transforms to a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. The two-dimensional version of the model (one-dimensional interface) is considered, mainly in the adiabatic limit of very slow driving. On length scales shorter than a crossover length (which grows with the strength of surface tension), the effective interface roughness exponent $zeta$ is $simeq 1.20$, close to the expected value for the universality class of the quenched Edwards-Wilkinson model. We find that the waiting times between avalanches are fully uncorrelated, as the wavelet transform of their autocorrelations scales as white noise. Similarly, detrended size-size correlations give a white-noise wavelet transform. Consideration of finite driving rates, still deep within the intermittent regime, shows the wavelet transform of correlations scaling as $1/f^{1.5}$ for intermediate frequencies. This behavior is ascribed to intra-avalanche correlations.
We study an asymptotic behavior of the return probability for the critical random matrix ensemble in the regime of strong multifractality. The return probability is expected to show critical scaling in the limit of large time or large system size. Using the supersymmetric virial expansion we confirm the scaling law and find analytical expressions for the fractal dimension of the wave functions $d_2$ and the dynamical scaling exponent $mu$. By comparing them we verify the validity of the Chalkers ansatz for dynamical scaling.
We study the localization properties of electrons moving on two-dimensional bi-partite lattices in the presence of disorder. The models investigated exhibit a chiral symmetry and belong to the chiral orthogonal (chO), chiral symplectic (chS) or chiral unitary (chU) symmetry class. The disorder is introduced via real random hopping terms for chO and chS, while complex random phases generate the disorder in the chiral unitary model. In the latter case an additional spatially constant, perpendicular magnetic field is also applied. Using a transfer-matrix-method, we numerically calculate the smallest Lyapunov exponents that are related to the localization length of the electronic eigenstates. From a finite-size scaling analysis, the logarithmic divergence of the localization length at the quantum critical point at E=0 is obtained. We always find for the critical exponent kappa, which governs the energy dependence of the divergence, a value close to 2/3. This result differs from the exponent kappa=1/2 found previously for a chiral unitary model in the absence of a constant magnetic field. We argue that a strong constant magnetic field changes the exponent kappa within the chiral unitary symmetry class by effectively restoring particle-hole symmetry even though a magnetic field induced transition from the ballistic to the diffusive regime cannot be fully excluded.
Critical scattering analyses for dilute antiferromagnets are made difficult by the lack of predicted theoretical line shapes beyond mean-field models. Nevertheless, with the use of some general scaling assumptions we have developed a procedure by which we can analyze the equilibrium critical scattering in these systems for H=0, the random-exchange Ising model, and, more importantly, for H>0, the random-field Ising model. Our new fitting approach, as opposed to the more conventional techniques, allows us to obtain the universal critical behavior exponents and amplitude ratios as well as the critical line shapes. We discuss the technique as applied to Fe(0.93)Zn(0.07)F2. The general technique, however, should be applicable to other problems where the scattering line shapes are not well understood but scaling is expected to hold.
Using the results of large scale numerical simulations we study the probability distribution of the pseudo critical temperature for the three-dimensional Edwards-Anderson Ising spin glass and for the fully connected Sherrington-Kirkpatrick model. We find that the behavior of our data is nicely described by straightforward finite-size scaling relations.