Exact Persistence Exponent for One-dimensional Potts Models with Parallel Dynamics

We obtain \theta_p(q) = 2\theta_s(q) for one-dimensional q-state ferromagnetic Potts models evolving under parallel dynamics at zero temperature from an initially disordered state, where \theta_p(q) is the persistence exponent for parallel dynamics and \theta_s(q) = -{1/8}+ \frac{2}{\pi^2}[cos^{-1}{(2-q)/q\sqrt{2}}]^2 [PRL, {\bf 75}, 751, (1995)], the persistence exponent under serial dynamics. This result is a consequence of an exact, albeit non-trivial, mapping of the evolution of configurations of Potts spins under parallel dynamics to the dynamics of two decoupled reaction diffusion systems.Comment: 13 pages Latex file, 5 postscript figure

Statistics of Multiple Sign Changes in a Discrete Non-Markovian Sequence

We study analytically the statistics of multiple sign changes in a discrete non-Markovian sequence ,\psi_i=\phi_i+\phi_{i-1} (i=1,2....,n) where \phi_i's are independent and identically distributed random variables each drawn from a symmetric and continuous distribution \rho(\phi). We show that the probability P_m(n) of m sign changes upto n steps is universal, i.e., independent of the distribution \rho(\phi). The mean and variance of the number of sign changes are computed exactly for all n>0. We show that the generating function {\tilde P}(p,n)=\sum_{m=0}^{\infty}P_m(n)p^m\sim \exp[-\theta_d(p)n] for large n where the `discrete' partial survival exponent \theta_d(p) is given by a nontrivial formula, \theta_d(p)=\log[{{\sin}^{-1}(\sqrt{1-p^2})}/{\sqrt{1-p^2}}] for 0\le p\le 1. We also show that in the natural scaling limit when m is large, n is large but but keeping x=m/n fixed, P_m(n)\sim \exp[-n \Phi(x)] where the large deviation function \Phi(x) is computed. The implications of these results for Ising spin glasses are discussed.Comment: 4 pages revtex, 1 eps figur

Non-collinear Magnetic Order in the Double Perovskites: Double Exchange on a Geometrically Frustrated Lattice

Double perovskites of the form A_2BB'O_6 usually involve a transition metal ion, B, with a large magnetic moment, and a non magnetic ion B'. While many double perovskites are ferromagnetic, studies on the underlying model reveal the possibility of antiferromagnetic phases as well driven by electron delocalisation. In this paper we present a comprehensive study of the magnetic ground state and T_c scales of the minimal double perovskite model in three dimensions using a combination of spin-fermion Monte Carlo and variational calculations. In contrast to two dimensions, where the effective magnetic lattice is bipartite, three dimensions involves a geometrically frustrated face centered cubic (FCC) lattice. This promotes non-collinear spiral states and `flux' like phases in addition to collinear anti-ferromagnetic order. We map out the possible magnetic phases for varying electron density, `level separation' epsilon_B - epsilon_B', and the crucial B'-B' (next neighbour) hopping t'.Comment: 15 pages pdflatex + 19 figs, revision: removed redundant comment

Exact ground state and kink-like excitations of a two dimensional Heisenberg antiferromagnet

A rare example of a two dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it is probably the first genuinely two-dimensional quantum system to exhibit domain-wall-like ``kink'' excitations normally found only in one-dimensional systems. In some limits it decouples into non-interacting chains, purely dynamically and not because of weakening of interchain couplings: indeed, paradoxically, this happens in the limit of strong coupling of the chains.Comment: 4 pages, revtex, 5 figures included via epsfi

Universality in the entanglement structure of ferromagnets

Systems of exchange-coupled spins are commonly used to model ferromagnets. The quantum correlations in such magnets are studied using tools from quantum information theory. Isotropic ferromagnets are shown to possess a universal low-temperature density matrix which precludes entanglement between spins, and the mechanism of entanglement cancellation is investigated, revealing a core of states resistant to pairwise entanglement cancellation. Numerical studies of one-, two-, and three-dimensional lattices as well as irregular geometries showed no entanglement in ferromagnets at any temperature or magnetic field strength.Comment: 4 pages, 2 figure

Exact Occupation Time Distribution in a Non-Markovian Sequence and Its Relation to Spin Glass Models

We compute exactly the distribution of the occupation time in a discrete {\em non-Markovian} toy sequence which appears in various physical contexts such as the diffusion processes and Ising spin glass chains. The non-Markovian property makes the results nontrivial even for this toy sequence. The distribution is shown to have non-Gaussian tails characterized by a nontrivial large deviation function which is computed explicitly. An exact mapping of this sequence to an Ising spin glass chain via a gauge transformation raises an interesting new question for a generic finite sized spin glass model: at a given temperature, what is the distribution (over disorder) of the thermally averaged number of spins that are aligned to their local fields? We show that this distribution remains nontrivial even at infinite temperature and can be computed explicitly in few cases such as in the Sherrington-Kirkpatrick model with Gaussian disorder.Comment: 10 pages Revtex (two-column), 1 eps figure (included

Mechanical and electrochemical properties of multiple-layer diode laser cladding of 316L stainless steel

In the present investigation, a detailed mechanical and electrochemical properties of multiple-layer laser clad 316L stainless steel (from the powders produced by gas atomized route) has been carried out. Multiple-layer laser cladding of 316L stainless steel has been conducted using a diode laser. The mechanical property (rmcrohardness) of the fabricated product has been evaluated using a microhardness testing machine and correlated with the process parameters. The electrochemical property, mainly pitting corrosion resistance of the fabricated layer corresponding to maximum microhardness (in a 3.56% NaCl solution) has been evaluated using standard potentiodynamic polarization testing. The microhardness of the laser assisted fabricated layers was found to vary from 170 to 278 VHN, increased with decrease in applied power density and increase in scan speed and was higher than that of conventionally processed 316L (155 VHN). The superior microhardness value is attributed to grain refinement associated with laser melting and rapid solidification. The critical potential to pit formation (E-PP1) was measured to be 550 mV saturated calomel electrode (SCE) and superior to the conventionally processed 316L stainless steel (445 mV (SCE)). (c) 2005 Elsevier B.V. All rights reserved

Condensation Transition in Polydisperse Hard Rods

We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles, referred to as $p$-spheres, have a linear size that behaves as $v_i^{1/p}$ and our model thus represents a gas of polydisperse hard rods with variable diameters $v_i^{1/p}$. We show that our model admits a factorized steady state distribution which provides the size distribution that minimizes the free energy of a polydisperse hard rod system, under the constraints of fixed $N$ and $V$. Complementary approaches (explicit construction of the steady state distribution on the one hand ; density functional theory on the other hand) completely and consistently specify the behaviour of the system. A real space condensation transition is shown to take place for $p>1$: beyond a critical density a macroscopic aggregate is formed and coexists with a critical fluid phase. Our work establishes the bridge between stochastic mass transport approaches and the optimal polydispersity of hard sphere fluids studied in previous articles