arXiv subjects

S. L. A. de Queiroz

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

47 records · Page 3Linked to original sources

arXiv1998

Domain size effects in Barkhausen noise

The possible existence of self-organized criticality in Barkhausen noise is investigated theoretically through a single interface model, and experimentally from measurements in amorphous magnetostrictive ribbon Metglas 2605TCA under stress. Contrary to previous interpretations in the literature, both simulation and experiment indicate that the presence of a cutoff in the avalanche size distribution may be attributed to finite size effects.

cond-mat.stat-mech↗

arXiv1998

Connectivity-dependent properties of diluted sytems in a transfer-matrix description

We introduce a new approach to connectivity-dependent properties of diluted systems, which is based on the transfer-matrix formulation of the percolation problem. It simultaneously incorporates the connective properties reflected in non-zero matrix elements and allows one to use standard random-matrix multiplication techniques. Thus it is possible to investigate physical processes on the percolation structure with the high efficiency and precision characteristic of transfer-matrix methods, while avoiding disconnections. The method is illustrated for two-dimensional site percolation by calculating (i) the critical correlation length along the strip, and the finite-size longitudinal DC conductivity: (ii) at the percolation threshold, and (iii) very near the pure-system limit.

cond-mat.stat-mech↗

arXiv1997

Universality and logarithmic corrections in two-dimensional random Ising ferromagnets

We address the question of weak versus strong universality scenarios for the random-bond Ising model in two dimensions. A finite-size scaling theory is proposed, which explicitly incorporates $\ln L$ corrections ($L$ is the linear finite size of the system) to the temperature derivative of the correlation length. The predictions are tested by considering long, finite-width strips of Ising spins with randomly distributed ferromagnetic couplings, along which free energy, spin-spin correlation functions and specific heats are calculated by transfer-matrix methods. The ratio $γ/ν$ is calculated and has the same value as in the pure case; consequently conformal invariance predictions remain valid for this type of disorder. Semilogarithmic plots of correlation functions against distance yield average correlation lengths $ξ^{av}$, whose size dependence agrees very well with the proposed theory. We also examine the size dependence of the specific heat, which clearly suggestsa divergency in the thermodynamic limit. Thus our data consistently favour the Dotsenko-Shalaev picture of logarithmic corrections (enhancements) to pure system singularities, as opposed to the weak universality scenario.

cond-mat.stat-mech↗

arXiv1997

Logarithmic corrections to gap scaling in random-bond Ising strips

Numerical results for the first gap of the Lyapunov spectrum of the self-dual random-bond Ising model on strips are analysed. It is shown that finite-width corrections can be fitted very well by an inverse logarithmic form, predicted to hold when the Hamiltonian contains a marginal operator.

cond-mat.stat-mech↗

arXiv1996

On weak vs. strong universality in the two-dimensional random-bond Ising ferromagnet

We address the issue of universality in two-dimensional disordered Ising systems, by considering long, finite-width strips of ferromagnetic Ising spins with randomly distributed couplings. We calculate the free energy and spin-spin correlation functions (from which averaged correlation lengths, $ξ^{ave}$, are computed) by transfer-matrix methods. An {\it ansatz} for the size-dependence of logarithmic corrections to $ξ^{ave}$ is proposed. Data for both random-bond and site-diluted systems show that pure system behaviour (with $ν=1$) is recovered if these corrections are incorporated, discarding the weak--universality scenario.

cond-mat↗

arXiv1996

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

We consider long strips of finite width $L \leq 13$ sites of ferromagnetic Ising spins with random couplings distributed according to the binary distribution: $P(J_{ij})= {1 \over 2} ( δ(J_{ij} -J_0) + δ(J_{ij} -rJ_0) ) ,\ 0 < r < 1 $. Spin-spin correlation functions $ <σ_{0} σ_{R}>$ along the ``infinite'' direction are computed by transfer-matrix methods, at the critical temperature of the corresponding two-dimensional system, and their probability distribution is investigated. We show that, although in-sample fluctuations do not die out as strip length is increased, averaged values converge satisfactorily. These latter are very close to the critical correlation functions of the pure Ising model, in agreement with recent Monte-Carlo simulations. A scaling approach is formulated, which provides the essential aspects of the $R$-- and $L$-- dependence of the probability distribution of $\ln <σ_{0} σ_{R}>$, including the result that the appropriate scaling variable is $R/L$. Predictions from scaling theory are borne out by numerical data, which show the probability distribution of $\ln <σ_{0} σ_{R}>$ to be remarkably skewed at short distances, approaching a Gaussian only as $R/L \gg 1$ .

cond-mat↗

arXiv1995

Search for Kosterlitz-Thouless transition in a triangular Ising antiferromagnet with further-neighbour ferromagnetic interactions

We investigate an antiferromagnetic triangular Ising model with anisotropic ferromagnetic interactions between next-nearest neighbours, originally proposed by Kitatani and Oguchi (J. Phys. Soc. Japan {\bf 57}, 1344 (1988)). The phase diagram as a function of temperature and the ratio between first- and second- neighbour interaction strengths is thoroughly examined. We search for a Kosterlitz-Thouless transition to a state with algebraic decay of correlations, calculating the correlation lengths on strips of width up to 15 sites by transfer-matrix methods. Phenomenological renormalization, conformal invariance arguments, the Roomany-Wyld approximation and a direct analysis of the scaled mass gaps are used. Our results provide limited evidence that a Kosterlitz-Thouless phase is present. Alternative scenarios are discussed.

cond-mat↗

arXiv1995

Domain scaling and marginality breaking in the random field Ising model

A scaling description is obtained for the $d$--dimensional random field Ising model from domains in a bar geometry. Wall roughening removes the marginality of the $d=2$ case, giving the $T=0$ correlation length $ξ\sim \exp\left(A h^{-γ}\right)$ in $d=2$, and for $d=2+ε$ power law behaviour with $ν= 2/εγ$, $h^\star \sim ε^{1/γ}$. Here, $γ= 2,4/3$ (lattice, continuum) is one of four rough wall exponents provided by the theory. The analysis is substantiated by three different numerical techniques (transfer matrix, Monte Carlo, ground state algorithm). These provide for strips up to width $L=11$ basic ingredients of the theory, namely free energy, domain size, and roughening data and exponents.

cond-mat↗

arXiv1995

Scaling treatment of the random field Ising model

Analytic phenomenological scaling is carried out for the random field Ising model in general dimensions using a bar geometry. Domain wall configurations and their decorated profiles and associated wandering and other exponents $(ζ,γ,δ,μ)$ are obtained by free energy minimization. Scaling between different bar widths provides the renormalization group (RG) transformation. Its consequences are (1) criticality at $h=T=0$ in $d \leq 2$ with correlation length $ξ(h,T)$ diverging like $ξ(h,0) \propto h^{-2/(2-d)}$ for $d<2$ and $ξ(h,0) \propto \exp[1/(c_1γh^γ)]$ for $d=2$, where $c_1$ is a decoration constant; (2) criticality in $d = 2+ε$ dimensions at $T=0$, $h^{\ast}= (ε/2c_1)^{1/γ}$, where $ξ\propto [(s-s^{\ast})/s]^{-2ε/γ}$, $s \equiv h^γ$. Finite temperature generalizations are outlined. Numerical transfer matrix calculations and results from a ground state algorithm adapted for strips in $d=2$ confirm the ingredients which provide the RG description.

cond-mat↗

arXiv1994

Correlation decay and conformal anomaly in the two-dimensional random-bond Ising ferromagnet

The two-dimensional random-bond Ising model is numerically studied on long strips by transfer-matrix methods. It is shown that the rate of decay of correlations at criticality, as derived from averages of the two largest Lyapunov exponents plus conformal invariance arguments, differs from that obtained through direct evaluation of correlation functions. The latter is found to be, within error bars, the same as in pure systems. Our results confirm field-theoretical predictions. The conformal anomaly $c$ is calculated from the leading finite-width correction to the averaged free energy on strips. Estimates thus obtained are consistent with $c=1/2$, the same as for the pure Ising model.

cond-mat↗

arXiv1994

Transfer-matrix scaling from disorder-averaged correlation lengths for diluted Ising systems

A transfer matrix scaling technique is developed for randomly diluted systems, and applied to the site-diluted Ising model on a square lattice in two dimensions. For each allowed disorder configuration between two adjacent columns, the contribution of the respective transfer matrix to the decay of correlations is considered only as far as the ratio of its two largest eigenvalues, allowing an economical calculation of a configuration-averaged correlation length. Standard phenomenological-renormalisation procedures are then used to analyse aspects of the phase boundary which are difficult to assess accurately by alternative methods. For magnetic site concentration $p$ close to $p_c$, the extent of exponential behaviour of the $T_c \times p$ curve is clearly seen for over two decades of variation of $p - p_c$. Close to the pure-system limit, the exactly-known reduced slope is reproduced to a very good approximation, though with non-monotonic convergence. The averaged correlation lengths are inserted into the exponent-amplitude relationship predicted by conformal invariance to hold at criticality. The resulting exponent $η$ remains near the pure value (1/4) for all intermediate concentrations until it crosses over to the percolation value at the threshold.

cond-mat↗