arXiv subjects

S. L. A. de Queiroz

Publications and source records attributed to S. L. A. de Queiroz.

At least 37 records · Page 2Linked to original sources

arXiv2008

Quantum Diffusion and Localization in Disordered Electronic Systems

The diffusion of electronic wave packets in one-dimensional systems with on-site, binary disorder is numerically investigated within the framework of a single-band tight-binding model. Fractal properties are incorporated by assuming that the distribution of distances $\ell$ between consecutive impurities obeys a power law, $P(\ell) \sim \ell^{-α}$. For suitable ranges of $α$, one finds system-wide anomalous diffusion. Asymmetric diffusion effects are introduced through the application of an external electric field, leading to results similar to those observed in the case of photogenerated electron-hole plasmas in tilted InP/InGaAs/InP quantum wells.

cond-mat.dis-nn↗

arXiv2008

Wavelet transforms in a critical interface model for Barkhausen noise

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 $ζ$ 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.

cond-mat.stat-mech↗

arXiv2006

Properties of the multicritical point of +/- J Ising spin glasses on the square lattice

We use numerical transfer-matrix methods to investigate properties of the multicriticalpoint of binary Ising spin glasses on a square lattice, whose location we assume to be given exactly by a conjecture advanced by Nishimori and Nemoto. We calculate the two largest Lyapunov exponents, as well as linear and non-linear zero-field uniform susceptibilities, on strip of widths $4 \leq L \leq 16$ sites, from which we estimate the conformal anomaly $c$, the decay-of-correlations exponent $η$, and the linear and non-linear susceptibility exponents $γ/ν$ and $γ^{nl}/ν$, with the help of finite-size scaling and conformal invariance concepts. Our results are: $c=0.46(1)$; $0.187 \lesssim η\lesssim 0.196$; $γ/ν=1.797(5)$; $γ^{nl}/ν=5.59(2)$. A direct evaluation of correlation functions on the strip geometry, and of the statistics of the zeroth moment of the associated probability distribution, gives $η=0.194(1)$, consistent with the calculation via Lyapunov exponents. Overall, these values tend to be inconsistent with the universality class of percolation, though by small amounts. The scaling relation $γ^{nl}/ν=2 γ/ν+d$ (with space dimensionality $d=2$) is obeyed to rather good accuracy, thus showing no evidence of multiscaling behavior of the susceptibilities.

cond-mat.stat-mech↗

arXiv2006

Logarithmic corrections to correlation decay in two-dimensional random-bond Ising systems

The statistics of critical spin-spin correlation functions in Ising systems with non-frustrated disorder are investigated on a strip geometry, via numerical transfer-matrix techniques. Conformal invariance concepts are used, in order to test for logarithmic corrections to pure power-law decay against distance. Fits of our data to conformal-invariance expressions, specific to logarithmic corrections to correlations on strips, give results with the correct sign, for the moments of order $n=0-4$ of the correlation-function distribution. We find an interval of disorder strength along which corrections to pure-system behavior can be decomposed into the product of a known $n$-dependent factor and an approximately $n$-independent one, in accordance with predictions. A phenomenological fitting procedure is proposed, which takes partial account of subdominant terms of correlation-function decay on strips. In the low-disorder limit, it gives results in fairly good agreement with theoretical predictions, provided that an additional assumption is made.

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arXiv2006

Anomalous dynamics in two- and three- dimensional Heisenberg-Mattis spin glasses

We investigate the spectral and localization properties of unmagnetized Heisenberg-Mattis spin glasses, in space dimensionalities $d=2$ and 3, at T=0. We use numerical transfer-matrix methods combined with finite-size scaling to calculate Lyapunov exponents, and eigenvalue-counting theorems, coupled with Gaussian elimination algorithms, to evaluate densities of states. In $d=2$ we find that all states are localized, with the localization length diverging as $ω^{-1}$, as energy $ω\to 0$. Logarithmic corrections to density of states behave in accordance with theoretical predictions. In $d=3$ the density-of-states dependence on energy is the same as for spin waves in pure antiferromagnets, again in agreement with theoretical predictions, though the corresponding amplitudes differ.

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arXiv2006

Multicritical point of Ising spin glasses on triangular and honeycomb lattices

The behavior of two-dimensional Ising spin glasses at the multicritical point on triangular and honeycomb lattices is investigated, with the help of finite-size scaling and conformal-invariance concepts. We use transfer-matrix methods on long strips to calculate domain-wall energies, uniform susceptibilities, and spin-spin correlation functions. Accurate estimates are provided for the location of the multicritical point on both lattices, which lend strong support to a conjecture recently advanced by Takeda, Sasamoto, and Nishimori. Correlation functions are shown to obey rather strict conformal-invariance requirements, once suitable adaptations are made to account for geometric aspects of the transfer-matrix description of triangular and honeycomb lattices. The universality class of critical behavior upon crossing the ferro-paramagnetic phase boundary is probed, with the following estimates for the associated critical indices: $ν=1.49(2)$, $γ=2.71(4)$, $η_1= 0.183(3)$, distinctly different from the percolation values.

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arXiv2005

Roughness of time series in a critical interface model

We study roughness probability distribution functions (PDFs) of the time signal for a critical interface model, which is known to provide a good description of Barkhausen noise in soft ferromagnets. Starting with time ``windows'' of data collection much larger than the system's internal ``loading time'' (related to demagnetization effects), we show that the initial Gaussian shape of the PDF evolves into a double-Gaussian structure as window width decreases. We supply a physical explanation for such structure, which is compatible with the observed numerical data. Connections to experiment are suggested.

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arXiv2004

Search for universal roughness distributions in a critical interface model

We study the probability distributions of interface roughness, sampled among successive equilibrium configurations of a single-interface model used for the description of Barkhausen noise in disordered magnets, in space dimensionalities $d=2$ and 3. The influence of a self-regulating (demagnetization) mechanism is investigated, and evidence is given to show that it is irrelevant, which implies that the model belongs to the Edwards-Wilkinson universality class. We attempt to fit our data to the class of roughness distributions associated to $1/f^α$ noise. Periodic, free, ``window'', and mixed boundary conditions are examined, with rather distinct results as regards quality of fits to $1/f^α$ distributions.

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arXiv2003

Dimensional crossover and universal roughness distributions in Barkhausen noise

We investigate the dimensional crossover of scaling properties of avalanches (domain-wall jumps) in a single-interface model, used for the description of Barkhausen noise in disordered magnets. By varying the transverse aspect ratio $A=L_y/L_x$ of simulated samples, the system dimensionality changes from two to three. We find that perturbing away from $d=2$ is a relevant field. The exponent $τ$ characterizing the power-law scaling of avalanche distributions varies between $1.06(1)$ for $d=2$ and $1.275(15)$ for $d=3$, according to a crossover function $f(x)$, $x \equiv (L_x^{-1})^ϕ/A$, with $ϕ=0.95(3)$. We discuss the possible relevance of our results to the interpretation of thin-film measurements of Barkhausen noise. We also study the probability distributions of interface roughness, sampled among successive equilibrium configurations in the Barkhausen noise regime. Attempts to fit our data to the class of universality distributions associated to $1/f^α$ noise give $α\simeq 1-1.1$ for $d=2$ and 3 (provided that suitable boundary conditions are used in the latter case).

cond-mat.stat-mech↗

arXiv2003

Correlation--function distributions at the Nishimori point of two-dimensional Ising spin glasses

The multicritical behavior at the Nishimori point of two-dimensional Ising spin glasses is investigated by using numerical transfer-matrix methods to calculate probability distributions $P(C)$ and associated moments of spin-spin correlation functions $C$ on strips. The angular dependence of the shape of correlation function distributions $P(C)$ provides a stringent test of how well they obey predictions of conformal invariance; and an even symmetry of $(1-C) P(C)$ reflects the consequences of the Ising spin-glass gauge (Nishimori) symmetry. We show that conformal invariance is obeyed in its strictest form, and the associated scaling of the moments of the distribution is examined, in order to assess the validity of a recent conjecture on the exact localization of the Nishimori point. Power law divergences of $P(C)$ are observed near C=1 and C=0, in partial accord with a simple scaling scheme which preserves the gauge symmetry.

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arXiv2002

Failure of single-parameter scaling of wave functions in Anderson localization

We show how to use properties of the vectors which are iterated in the transfer-matrix approach to Anderson localization, in order to generate the statistical distribution of electronic wavefunction amplitudes at arbitary distances from the origin of $L^{d-1} \times \infty$ disordered systems. For $d=1$ our approach is shown to reproduce exact diagonalization results available in the literature. In $d=2$, where strips of width $ L \leq 64$ sites were used, attempted fits of gaussian (log-normal) forms to the wavefunction amplitude distributions result in effective localization lengths growing with distance, contrary to the prediction from single-parameter scaling theory. We also show that the distributions possess a negative skewness $S$, which is invariant under the usual histogram-collapse rescaling, and whose absolute value increases with distance. We find $0.15 \lesssim -S \lesssim 0.30$ for the range of parameters used in our study, .

cond-mat.dis-nn↗

arXiv2002

Finite-size investigation of scaling corrections in the square-lattice three-state Potts antiferromagnet square-lattice three-state Potts antiferromagnet

We investigate the finite-temperature corrections to scaling in the three-state square-lattice Potts antiferromagnet, close to the critical point at T=0. Numerical diagonalization of the transfer matrix on semi-infinite strips of width $L$ sites, $4 \leq L \leq 14$, yields finite-size estimates of the corresponding scaled gaps, which are extrapolated to $L\to\infty$. Owing to the characteristics of the quantities under study, we argue that the natural variable to consider is $x \equiv L e^{-2β}For the extrapolated scaled gaps we show that square-root corrections, in the variable $x$, are present, and provide estimates for the numerical values of the amplitudes of the first-- and second--order correction terms, for both the first and second scaled gaps. We also calculate the third scaled gap of the transfer matrix spectrum at T=0, and find an extrapolated value of the decay-of-correlations exponent, $η_3=2.00(1)$. This is at odds with earlier predictions, to the effect that the third relevant operator in the problem would give $η_{{\bf P}_{\rm stagg}}=3$, corresponding to the staggered polarization.

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arXiv2001

Finite driving rates in interface models of Barkhausen noise

We consider a single-interface model for the description of Barkhausen noise in soft ferromagnetic materials. Previously, the model had been used only in the adiabatic regime of infinitely slow field ramping. We introduce finite driving rates and analyze the scaling of event sizes and durations for different regimes of the driving rate. Coexistence of intermittency, with non-trivial scaling laws, and finite-velocity interface motion is observed for high enough driving rates. Power spectra show a decay $\sim ω^{-t}$, with $t<2$ for finite driving rates, revealing the influence of the internal structure of avalanches.

cond-mat.stat-mech↗

arXiv2001

Correlation functions, free energies and magnetizations in the two-dimensional random-field Ising model

Transfer-matrix methods are used to calculate spin-spin correlation functions ($G$), Helmholtz free energies ($f$) and magnetizations ($m$) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature $T_{c 0}$, on long strips of width $L = 3 - 18$ sites, for binary field distributions. Analysis of the probability distributions of $G$ for varying spin-spin distances $R$ shows that describing the decay of their averaged values by effective correlation lengths is a valid procedure only for not very large $R$. Connections between field-- and correlation function distributions at high temperatures are established, yielding approximate analytical expressions for the latter, which are used for computation of the corresponding structure factor. It is shown that, for fixed $R/L$, the fractional widths of correlation-function distributions saturate asymptotically with $L^{-2.2}$. Considering an added uniform applied field $h$, a connection between $f(h)$, $m(h)$, the Gibbs free energy $g(m)$ and the distribution function for the uniform magnetization in zero uniform field, $P_0(m)$, is derived and first illustrated for pure systems, and then applied for non-zero random field. From finite-size scaling and crossover arguments, coupled with numerical data, it is found that the width of $P_0(m)$ varies against (non-vanishing, but small) random-field intensity $H_0$ as $H_0^{-3/7}$.

cond-mat.stat-mech↗

arXiv2000

Reentrant behaviour and universality in the Anderson transition

The three-dimensional Anderson model with a rectangular distribution of site disorder displays two distinct localization-delocalization transitions, against varying disorder intensity, for a relatively narrow range of Fermi energies. Such transitions are studied through the calculation of localization lengths of quasi-- one-dimensional systems by transfer-matrix methods, and their analysis by finite-size scaling techniques. For the transition at higher disorder we find the localization-length exponent $ν=1.60(5)$ and the limiting scaled localization-length amplitude $Λ_0=0.57(1)$, strongly suggesting universality with the transition at the band centre, for which currently accepted values are $ν=1.57(2)$ and $Λ_0=0.576(2)$. For the lower (reentrant) transition, we estimate $ν=1.55(15)$ and $Λ_0=0.55(5)$, still compatible with universality but much less precise, partly owing to significant finite-size corrections.

cond-mat.dis-nn↗

arXiv1999

Correlation functions in the two-dimensional random-field Ising model

Transfer-matrix methods are used to study the probability distributions of spin-spin correlation functions $G$ in the two-dimensional random-field Ising model, on long strips of width $L = 3 - 15$ sites, for binary field distributions at generic distance $R$, temperature $T$ and field intensity $h_0$. For moderately high $T$, and $h_0$ of the order of magnitude used in most experiments, the distributions are singly-peaked, though rather asymmetric. For low temperatures the single-peaked shape deteriorates, crossing over towards a double-$δ$ ground-state structure. A connection is obtained between the probability distribution for correlation functions and the underlying distribution of accumulated field fluctuations. Analytical expressions are in good agreement with numerical results for $R/L \gtrsim 1$, low $T$, $h_0$ not too small, and near G=1. From a finite-size {\it ansatz} at $T=T_c (h_0=0)$, $h_0 \to 0$, averaged correlation functions are predicted to scale with $L^y h_0$, $y =7/8$. From numerical data we estimate y=0.875 \pm 0.025$, in excellent agreement with theory. In the same region, the RMS relative width $W$ of the probability distributions varies for fixed $R/L=1$ as $W \sim h_0^κ f(L h_0^u)$ with $κ\simeq 0.45$, $u \simeq 0.8$ ; $f(x)$ appears to saturate when $x \to \infty$, thus implying $W \sim h_0^κ$ in $d=2$.

cond-mat.stat-mech↗

arXiv1999

Universality, frustration and conformal invariance in two-dimensional random Ising magnets

We consider long, finite-width strips of Ising spins with randomly distributed couplings. Frustration is introduced by allowing both ferro- and antiferromagnetic interactions. Free energy and spin-spin correlation functions are calculated by transfer-matrix methods. Numerical derivatives and finite-size scaling concepts allow estimates of the usual critical exponents $γ/ν$, $α/ν$ and $ν$ to be obtained, whenever a second-order transition is present. Low-temperature ordering persists for suitably small concentrations of frustrated bonds, with a transition governed by pure--Ising exponents. Contrary to the unfrustrated case, subdominant terms do not fit a simple, logarithmic-enhancement form. Our analysis also suggests a vertical critical line at and below the Nishimori point. Approaching this point along either the temperature axis or the Nishimori line, one finds non-diverging specific heats. A percolation-like ratio $γ/ν$ is found upon analysis of the uniform susceptibility at the Nishimori point. Our data are also consistent with frustration inducing a breakdown of the relationship between correlation-length amplitude and critical exponents, predicted by conformal invariance for pure systems.

cond-mat.stat-mech↗

arXiv1998

Field-induced Ordering in Critical Antiferromagnets

Transfer-matrix scaling methods have been used to study critical properties of field-induced phase transitions of two distinct two-dimensional antiferromagnets with discrete-symmetry order parameters: triangular-lattice Ising systems (TIAF) and the square-lattice three-state Potts model (SPAF-3). Our main findings are summarised as follows. For TIAF, we have shown that the critical line leaves the zero-temperature, zero -field fixed point at a finite angle. Our best estimate of the slope at the origin is $(dT_c/dH)_{T=H=0} = 4.74 \pm 0.15$. For SPAF-3 we provided evidence that the zero-field correlation length diverges as $ξ(T \to 0, H=0) \simeq \exp (a/T^{x})$, with $x=1.08 \pm 0.13$, through analysis of the critical curve at $H \neq 0$ plus crossover arguments. For SPAF-3 we have also ascertained that the conformal anomaly and decay-of-correlations exponent behave as: (a) H=0: $c=1, η=1/3$; (b) $H \neq 0: c=1/2, η=1/4$.

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