Algebraic Aspects of Abelian Sandpile Models

The abelian sandpile models feature a finite abelian group G generated by the operators corresponding to particle addition at various sites. We study the canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G, and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of toppling matrix. We construct scalar functions, linear in height variables of the pile, that are invariant toppling at any site. These invariants provide convenient coordinates to label the recurrent configurations of the sandpile. For an L X L square lattice, we show that g = L. In this case, we observe that the system has nontrivial symmetries coming from the action of the cyclotomic Galois group of the (2L+2)th roots of unity which operates on the set of eigenvalues of the toppling matrix. These eigenvalues are algebraic integers, whose product is the order |G|. With the help of this Galois group, we obtain an explicit factorizaration of |G|. We also use it to define other simpler, though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3

A Study of Noon F2 Ionization in Relation to Geomagnetic Co-ordinates

The relation of F2 layer noon critical frequency with magnetic dip and geomagnetic latitude is studied for constant values of solar zenithal angle. The constant-x plots show two maxima situated on the two sides of the magnetic equator. An asymmetry between the northern and southern hemispheres is also revealed. For chosen values of solar zenith distance the ratio of noon fF2 at sunspot maximum to that at sunspot minimum is studied in relation to magnetic dip. The ratio is found to vary with magnetic dip displaying a minimum to the north of the magnetic equator

Tailoring symmetry groups using external alternate fields

Macroscopic systems with continuous symmetries subjected to oscillatory fields have phases and transitions that are qualitatively different from their equilibrium ones. Depending on the amplitude and frequency of the fields applied, Heisenberg ferromagnets can become XY or Ising-like -or, conversely, anisotropies can be compensated -thus changing the nature of the ordered phase and the topology of defects. The phenomena can be viewed as a dynamic form of "order by disorder".Comment: 4 pages, 2 figures finite dimension and selection mechanism clarifie

Logarithmic corrections of the avalanche distributions of sandpile models at the upper critical dimension

We study numerically the dynamical properties of the BTW model on a square lattice for various dimensions. The aim of this investigation is to determine the value of the upper critical dimension where the avalanche distributions are characterized by the mean-field exponents. Our results are consistent with the assumption that the scaling behavior of the four-dimensional BTW model is characterized by the mean-field exponents with additional logarithmic corrections. We benefit in our analysis from the exact solution of the directed BTW model at the upper critical dimension which allows to derive how logarithmic corrections affect the scaling behavior at the upper critical dimension. Similar logarithmic corrections forms fit the numerical data for the four-dimensional BTW model, strongly suggesting that the value of the upper critical dimension is four.Comment: 8 pages, including 9 figures, accepted for publication in Phys. Rev.

Percolation Systems away from the Critical Point

This article reviews some effects of disorder in percolation systems even away from the critical density p_c. For densities below p_c, the statistics of large clusters defines the animals problem. Its relation to the directed animals problem and the Lee-Yang edge singularity problem is described. Rare compact clusters give rise to Griffiths singuraties in the free energy of diluted ferromagnets, and lead to a very slow relaxation of magnetization. In biassed diffusion on percolation clusters, trapping in dead-end branches leads to asymptotic drift velocity becoming zero for strong bias, and very slow relaxation of velocity near the critical bias field.Comment: Minor typos fixed. Submitted to Praman

An Investigation on Structural and Electrical Properties of RF-Sputtered Molybdenum Thin Film Deposited on Different Substrates

AbstractMolybdenum (Mo) is the prominent choice as the back contact for various thin film solar cells such as CIGS, CZTS and CdTe. Physical vapour deposition (PVD) technique especially sputtering process has been chosen as the foremost method to deposit Mo thin film on top of desired substrate due to ease of parametric control of growth conditions. In this paper, we reported the effect of various RF power, operating pressure as well as temperature on Mo films on top of Mo sheet and soda lime glass (SLG) deposited using RF magnetron sputtering. Uniform surface morphology was obtained as RF power, operating pressure and deposition temperature were optimised. However, at higher deposition temperature less uniform surface was observed. XRD pattern of Mo films showed two different peak of <200> and <211> in case of Mo sheet and single peak <110> in case of SLG. While peak intensity varies as deposition condition varies in case of Mo films deposited on Mo sheet. Electrical properties of Mo films on both Mo sheet and SLG were improved as RF power and deposition temperature are optimised. On the other hand, electrical properties are affected as operating pressure increased. Lower resistivity of 1.2x10-9Ω.m and 6.65x10-6Ω.m were found in case of Mo films deposited on Mo sheet and SLG. Surface roughness of 0.017 nm-19.32nm were found in case of Mo films deposited on Mo sheet and 0.002 nm-5.04nm were found in case of SLG. Roughness increased as RF power and deposition temperature increased. However, roughness decreased as operating pressure increased

Lyapunov exponents and transport in the Zhang model of Self-Organized Criticality

We discuss the role played by the Lyapunov exponents in the dynamics of Zhang's model of Self-Organized Criticality. We show that a large part of the spectrum (slowest modes) is associated with the energy transpor in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum and relate the scaling exponent to the scaling of quantities like avalanche size, duration, density of active sites, etc ...Comment: 33 pages, 6 figures, 1 table (to appear

Inversion Symmetry and Critical Exponents of Dissipating Waves in the Sandpile Model

Statistics of waves of topplings in the Sandpile model is analysed both analytically and numerically. It is shown that the probability distribution of dissipating waves of topplings that touch the boundary of the system obeys power-law with critical exponent 5/8. This exponent is not indeendent and is related to the well-known exponent of the probability distribution of last waves of topplings by exact inversion symmetry s -> 1/s.Comment: 5 REVTeX pages, 6 figure

Magnetic Anisotropy in Single Crystalline CeAu2_{2}In4_{4}

We have grown the single crystals of LaAu$_{2}$In$_{4}$ and CeAu$_{2}$In$_{4}$ by high temperature solution method and report on the anisotropic magnetic behavior of CeAu$_{2}$In$_{4}$ . The compounds crystallize in an orthorhombic structure with space group \textit {Pnma}. LaAu$_{2}$In$_{4}$ shows a Pauli-paramagnetic behavior. CeAu$_{2}$In$_{4}$ do not order down to 1.8 K. The easy axis of magnetization for CeAu$_{2}$In$_{4}$ is along [010] direction. The magnetization data is analyzed on the basis of crystalline electric field (CEF) model.Comment: 7 figures 4 page

Breakdown of Simple Scaling in Abelian Sandpile Models in One Dimension

We study the abelian sandpile model on decorated one dimensional chains. We determine the structure and the asymptotic form of distribution of avalanche-sizes in these models, and show that these differ qualitatively from the behavior on a simple linear chain. We find that the probability distribution of the total number of topplings $s$ on a finite system of size $L$ is not described by a simple finite size scaling form, but by a linear combination of two simple scaling forms $Prob_L(s) = 1/L f_1(s/L) + 1/L^2 f_2(s/L^2)$, for large $L$, where $f_1$ and $f_2$ are some scaling functions of one argument.Comment: 10 pages, revtex, figures include