5,092 research outputs found
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 , with the constraint of a fixed
total volume , being the total number of particles. The
particles, referred to as -spheres, have a linear size that behaves as
and our model thus represents a gas of polydisperse hard rods with
variable diameters . 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 and . 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 : 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
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