117 research outputs found
Finite-Size Scaling in Two-dimensional Continuum Percolation Models
We test the universal finite-size scaling of the cluster mass order parameter
in two-dimensional (2D) isotropic and directed continuum percolation models
below the percolation threshold by computer simulations. We found that the
simulation data in the 2D continuum models obey the same scaling expression of
mass M to sample size L as generally accepted for isotropic lattice problems,
but with a positive sign of the slope in the ln-ln plot of M versus L. Another
interesting aspect of the finite-size 2D models is also suggested by plotting
the normalized mass in 2D continuum and lattice bond percolation models, versus
an effective percolation parameter, independently of the system structure (i.e.
lattice or continuum) and of the possible directions allowed for percolation
(i.e. isotropic or directed) in regions close to the percolation thresholds.
Our study is the first attempt to map the scaling behaviour of the mass for
both lattice and continuum model systems into one curve.Comment: 9 pages, Revtex, 2 PostScript figure
On the Aizenman exponent in critical percolation
The probabilities of clusters spanning a hypercube of dimensions two to seven
along one axis of a percolation system under criticality were investigated
numerically. We used a modified Hoshen--Kopelman algorithm combined with
Grassberger's "go with the winner" strategy for the site percolation. We
carried out a finite-size analysis of the data and found that the probabilities
confirm Aizenman's proposal of the multiplicity exponent for dimensions three
to five. A crossover to the mean-field behavior around the upper critical
dimension is also discussed.Comment: 5 pages, 4 figures, 4 table
Percolation in Models of Thin Film Depositions
We have studied the percolation behaviour of deposits for different
(2+1)-dimensional models of surface layer formation. The mixed model of
deposition was used, where particles were deposited selectively according to
the random (RD) and ballistic (BD) deposition rules. In the mixed one-component
models with deposition of only conducting particles, the mean height of the
percolation layer (measured in monolayers) grows continuously from 0.89832 for
the pure RD model to 2.605 for the pure RD model, but the percolation
transition belong to the same universality class, as in the 2- dimensional
random percolation problem. In two- component models with deposition of
conducting and isolating particles, the percolation layer height approaches
infinity as concentration of the isolating particles becomes higher than some
critical value. The crossover from 2d to 3d percolation was observed with
increase of the percolation layer height.Comment: 4 pages, 5 figure
Interface pinning and slow ordering kinetics on infinitely ramified fractal structures
We investigate the time dependent Ginzburg-Landau (TDGL) equation for a non
conserved order parameter on an infinitely ramified (deterministic) fractal
lattice employing two alternative methods: the auxiliary field approach and a
numerical method of integration of the equations of evolution. In the first
case the domain size evolves with time as , where is
the anomalous random walk exponent associated with the fractal and differs from
the normal value 2, which characterizes all Euclidean lattices. Such a power
law growth is identical to the one observed in the study of the spherical model
on the same lattice, but fails to describe the asymptotic behavior of the
numerical solutions of the TDGL equation for a scalar order parameter. In fact,
the simulations performed on a two dimensional Sierpinski Carpet indicate that,
after an initial stage dominated by a curvature reduction mechanism \`a la
Allen-Cahn, the system enters in a regime where the domain walls between
competing phases are pinned by lattice defects.
The lack of translational invariance determines a rough free energy
landscape, the existence of many metastable minima and the suppression of the
marginally stable modes, which in translationally invariant systems lead to
power law growth and self similar patterns. On fractal structures as the
temperature vanishes the evolution is frozen, since only thermally activated
processes can sustain the growth of pinned domains.Comment: 16 pages+14 figure
SmartEx: a case study on user profiling and adaptation in exhibition booths
An investigation into user profiling and adaptation with exhibition booth as a case study is reported. First a review of the field of exhibitions and trade fairs and a summary introduction to adaptation and profiling are given. We then introduce three criteria for the evaluation of exhibition booth: effectiveness, efficiency and affect. Effectiveness is related the amount of information collected, efficiency is a measurement of the time taken to collect the information, and affect is the perception of the experience and the mood booth visitors have during and after their visit. We have selected these criteria to assess adaptive and profiled exhibition booths, we call smart exhibition (SmartEx). The assessment is performed with an experiment with three test conditions (non-profiled/non adaptive, profiled/non-adaptive and profiled adaptive presentations). Results of the experiment are presented along discussion. While there is significant improvements of effectiveness and efficiency between the two-first test conditions, the improvement is not significant for the last test condition, for reasons explained. As for the affect, the results show that it has an under-estimated importance in people minds and that it should be addressed more carefully
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
The role of the alloy structure in the magnetic behavior of granular systems
The effect of grain size, easy magnetization axis and anisotropy constant
distributions in the irreversible magnetic behavior of granular alloys is
considered. A simulated granular alloy is used to provide a realistic grain
structure for the Monte Carlo simulation of the ZFC-FC curves. The effect of
annealing and external field is also studied. The simulation curves are in good
agreement with the FC and ZFC magnetization curves measured on melt spun Cu-Co
ribbons.Comment: 13 pages, 10 figures, submitted to PR
Two-magnon bound state causes ultrafast thermally induced magnetisation switching.
There has been much interest recently in the discovery of thermally induced magnetisation switching using femtosecond laser excitation, where a ferrimagnetic system can be switched deterministically without an applied magnetic field. Experimental results suggest that the reversal occurs due to intrinsic material properties, but so far the microscopic mechanism responsible for reversal has not been identified. Using computational and analytic methods we show that the switching is caused by the excitation of two-magnon bound states, the properties of which are dependent on material factors. This discovery allows us to accurately predict the onset of switching and the identification of this mechanism will allow new classes of materials to be identified or designed for memory devices in the THz regime
Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q
The Q-state Potts model can be extended to noninteger and even complex Q in
the FK representation. In the FK representation the partition function,Z(Q,a),
is a polynomial in Q and v=a-1(a=e^-T) and the coefficients of this
polynomial,Phi(b,c), are the number of graphs on the lattice consisting of b
bonds and c connected clusters. We introduce the random-cluster transfer matrix
to compute Phi exactly on finite square lattices. Given the FK representation
of the partition function we begin by studying the critical Potts model
Z_{CP}=Z(Q,a_c), where a_c=1+sqrt{Q}. We find a set of zeros in the complex
w=sqrt{Q} plane that map to the Beraha numbers for real positive Q. We also
identify tilde{Q}_c(L), the value of Q for a lattice of width L above which the
locus of zeros in the complex p=v/sqrt{Q} plane lies on the unit circle. We
find that 1/tilde{Q}_c->0 as 1/L->0. We then study zeros of the AF Potts model
in the complex Q plane and determine Q_c(a), the largest value of Q for a fixed
value of a below which there is AF order. We find excellent agreement with
Q_c=(1-a)(a+3). We also investigate the locus of zeros of the FM Potts model in
the complex Q plane and confirm that Q_c=(a-1)^2. We show that the edge
singularity in the complex Q plane approaches Q_c as Q_c(L)~Q_c+AL^-y_q, and
determine the scaling exponent y_q. Finally, by finite size scaling of the
Fisher zeros near the AF critical point we determine the thermal exponent y_t
as a function of Q in the range 2<Q<3. We find that y_t is a smooth function of
Q and is well fit by y_t=(1+Au+Bu^2)/(C+Du) where u=u(Q). For Q=3 we find
y_t~0.6; however if we include lattices up to L=12 we find y_t~0.50.Comment: to appear in Physical Review
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