Enhanced grain surface effect on magnetic properties of nanometric La0.7Ca0.3MnO3 manganite : Evidence of surface spin freezing of manganite nanoparticles

We have investigated the effect of nanometric grain size on magnetic properties of single phase, nanocrystalline, granular La0.7Ca0.3MnO3 (LCMO) sample. We have considered core-shell structure of our LCMO nanoparticles, which can explain its magnetic properties. From the temperature dependence of field cooled (FC) and zero-field cooled (ZFC) dc magnetization (DCM), the magnetic properties could be distinguished into two regimes: a relatively high temperature regime T > 40 K where the broad maximum of ZFC curve (at T = Tmax) is associated with the blocking of core particle moments, whereas the sharp maximum (at T = TS) is related to the freezing of surface (shell) spins. The unusual shape of M (H) loop at T = 1.5 K, temperature dependent feature of coercive field and remanent magnetization give a strong support of surface spin freezing that are occurring at lower temperature regime (T < 40 K) in this LCMO nanoparticles. Additionally, waiting time (tw) dependence of ZFC relaxation measurements at T = 50 K show weak dependence of relaxation rate [S(t)] on tw and dM/dln(t) following a logarithmic variation on time. Both of these features strongly support the high temperature regime to be associated with the blocking of core moments. At T = 20 K, ZFC relaxation measurements indicates the existence of two different types of relaxation processes in the sample with S(t) attaining a maximum at the elapsed time very close to the wait time tw = 1000 sec, which is an unequivocal sign of glassy behavior. This age-dependent effect convincingly establish the surface spin freezing of our LCMO nanoparticles associated with a background of superparamagnetic (SPM) phase of core moments.Comment: 41 pages, 10 figure

Renormalization group approach to an Abelian sandpile model on planar lattices

One important step in the renormalization group (RG) approach to a lattice sandpile model is the exact enumeration of all possible toppling processes of sandpile dynamics inside a cell for RG transformations. Here we propose a computer algorithm to carry out such exact enumeration for cells of planar lattices in RG approach to Bak-Tang-Wiesenfeld sandpile model [Phys. Rev. Lett. {\bf 59}, 381 (1987)] and consider both the reduced-high RG equations proposed by Pietronero, Vespignani, and Zapperi (PVZ) [Phys. Rev. Lett. {\bf 72}, 1690 (1994)] and the real-height RG equations proposed by Ivashkevich [Phys. Rev. Lett. {\bf 76}, 3368 (1996)]. Using this algorithm we are able to carry out RG transformations more quickly with large cell size, e.g. $3 \times 3$ cell for the square (sq) lattice in PVZ RG equations, which is the largest cell size at the present, and find some mistakes in a previous paper [Phys. Rev. E {\bf 51}, 1711 (1995)]. For sq and plane triangular (pt) lattices, we obtain the only attractive fixed point for each lattice and calculate the avalanche exponent $\tau$ and the dynamical exponent $z$. Our results suggest that the increase of the cell size in the PVZ RG transformation does not lead to more accurate results. The implication of such result is discussed.Comment: 29 pages, 6 figure

Nonuniversal exponents in sandpiles with stochastic particle number transfer

We study fixed density sandpiles in which the number of particles transferred to a neighbor on relaxing an active site is determined stochastically by a parameter $p$. Using an argument, the critical density at which an active-absorbing transition occurs is found exactly. We study the critical behavior numerically and find that the exponents associated with both static and time-dependent quantities vary continuously with $p$.Comment: Some parts rewritten, results unchanged. To appear in Europhys. Let

Chaos in Sandpile Models

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the attractor of \textit{deterministic} models. We have shown that the (abelian) BTW sandpile model and the (non abelian) Zhang model posses different "weak chaos" exponents, so they may belong to different universality classes. We have also shown that \textit{stochasticity} destroys "weak chaos" exponents' effectiveness so it slows down the divergence of nearby configurations. Finally we show that getting off the critical point destroys this behavior of deterministic models.Comment: 5 pages, 6 figure

Order Parameter and Scaling Fields in Self-Organized Criticality

We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the order parameter and the relevant scaling fields in order to describe the critical behavior in terms of usual concepts of non equilibrium lattice models with steady-states. We point out the inconsistencies of previous mean-field approaches, which lead to different predictions. Numerical simulations confirm the validity of our results beyond mean-field theory.Comment: 4 RevTex pages and 2 postscript figure

Mathematical modelling of peritectic transformation in binary systems

A simple diffusional analysis of peritectic transformat-ion based on the linearized concentration gradient approximation and a rigorous numerical model of the peri-tectic transformation as well as the solid state homo-genization process following liquid depletion has been presented.The overall and interface mass balance equations are utilized to calculate the rate of movement of the interfaces in the finite geometry. The predictions of the present models, show a better agreement with the experi-mentally determined kinetic data from the Cd-Ag and Pd-Bi systems as compared to those by the earlier proposed 'models based on quasi-static interface or time-invariant or Laplacian concentration profiles. However, the computed kinetics differ from the observed rates of transformation at a later stage (-50% transformation), perhaps, due to the deviation from the idealized cell configuration consi-dered in the calculations

Clustering properties of a generalised critical Euclidean network

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a probability proportional to $k^\beta_i \ell^{\alpha}$. For $\alpha > -0.5$, the network is scale free at $\beta = 1$ with the degree distribution $P(k) \propto k^{-\gamma}$ and $\gamma = 3.0$ as in the Barab\'asi-Albert model ($\alpha =0, \beta =1$). We find a phase boundary in the $\alpha-\beta$ plane along which the network is scale-free. Interestingly, we find scale-free behaviour even for $\beta > 1$ for $\alpha < -0.5$ where the existence of a new universality class is indicated from the behaviour of the degree distribution and the clustering coefficients. The network has a small diameter in the entire scale-free region. The clustering coefficients emulate the behaviour of most real networks for increasing negative values of $\alpha$ on the phase boundary.Comment: 4 pages REVTEX, 4 figure

Quenched noise and over-active sites in sandpile dynamics

The dynamics of sandpile models are mapped to discrete interface equations. We study in detail the Bak-Tang-Wiesenfeld model, a stochastic model with random thresholds, and the Manna model. These are, respectively, discretizations of the quenched Edwards-Wilkinson equation with columnar, point-like and correlated noise, with the constraint that the interface velocity is either zero or exactly one. The constraint, embedded in the sandpile rules, gives rise to another noise component. This term has for the Bak-Tang-Wiesenfeld model long-range on-site correlations and reveals that with open boundary conditions there is no spatial translational invariance.Comment: 4 pages, 3 figure

Universality Classes in Isotropic, Abelian and non-Abelian, Sandpile Models

Universality in isotropic, abelian and non-abelian, sandpile models is examined using extensive numerical simulations. To characterize the critical behavior we employ an extended set of critical exponents, geometric features of the avalanches, as well as scaling functions describing the time evolution of average quantities such as the area and size during the avalanche. Comparing between the abelian Bak-Tang-Wiesenfeld model [P. Bak, C. Tang and K. Wiensenfeld, Phys. Rev. Lett. 59, 381 (1987)], and the non-abelian models introduced by Manna [S. S. Manna, J. Phys. A. 24, L363 (1991)] and Zhang [Y. C. Zhang, Phys. Rev. Lett. 63, 470 (1989)] we find strong indications that each one of these models belongs to a distinct universality class.Comment: 18 pages of text, RevTeX, additional 8 figures in 12 PS file