4,986 research outputs found
The Quantum Compass Model on the Square Lattice
Using exact diagonalizations, Green's function Monte Carlo simulations and
high-order perturbation theory, we study the low-energy properties of the
two-dimensional spin-1/2 compass model on the square lattice defined by the
Hamiltonian . When
, we show that, on clusters of dimension , the
low-energy spectrum consists of states which collapse onto each other
exponentially fast with , a conclusion that remains true arbitrarily close
to . At that point, we show that an even larger number of states
collapse exponentially fast with onto the ground state, and we present
numerical evidence that this number is precisely . We also extend
the symmetry analysis of the model to arbitrary spins and show that the
two-fold degeneracy of all eigenstates remains true for arbitrary half-integer
spins but does not apply to integer spins, in which cases eigenstates are
generically non degenerate, a result confirmed by exact diagonalizations in the
spin-1 case. Implications for Mott insulators and Josephson junction arrays are
briefly discussed.Comment: 8 pages, 8 figure
Identification of an RVB liquid phase in a quantum dimer model with competing kinetic terms
Starting from the mean-field solution of a spin-orbital model of LiNiO,
we derive an effective quantum dimer model (QDM) that lives on the triangular
lattice and contains kinetic terms acting on 4-site plaquettes and 6-site
loops. Using numerical exact diagonalizations and Green's function Monte Carlo
simulations, we show that the competition between these kinetic terms leads to
a resonating valence bond (RVB) state for a finite range of parameters. We also
show that this RVB phase is connected to the RVB phase identified in the
Rokhsar-Kivelson model on the same lattice in the context of a generalized
model that contains both the 6--site loops and a nearest-neighbor dimer
repulsion. These results suggest that the occurrence of an RVB phase is a
generic feature of QDM with competing interactions.Comment: 8 pages, 12 figure
Fat fractal percolation and k-fractal percolation
We consider two variations on the Mandelbrot fractal percolation model. In
the k-fractal percolation model, the d-dimensional unit cube is divided in N^d
equal subcubes, k of which are retained while the others are discarded. The
procedure is then iterated inside the retained cubes at all smaller scales. We
show that the (properly rescaled) percolation critical value of this model
converges to the critical value of ordinary site percolation on a particular
d-dimensional lattice as N tends to infinity. This is analogous to the result
of Falconer and Grimmett that the critical value for Mandelbrot fractal
percolation converges to the critical value of site percolation on the same
d-dimensional lattice. In the fat fractal percolation model, subcubes are
retained with probability p_n at step n of the construction, where (p_n) is a
non-decreasing sequence with \prod p_n > 0. The Lebesgue measure of the limit
set is positive a.s. given non-extinction. We prove that either the set of
connected components larger than one point has Lebesgue measure zero a.s. or
its complement in the limit set has Lebesgue measure zero a.s.Comment: 27 pages, 3 figure
Dissolution and phosphate-induced transformation of ZnO nanoparticles in synthetic saliva probed by AGNES without previous solid-liquid separation. Comparison with UF-ICP-MS
The variation over time of free Zn2+ ion concentration in stirred dispersions of ZnO nanoparticles (ZnO NPs) prepared in synthetic saliva at pH 6.80 and 37 degrees C was followed in situ (without solid liquid separation step) with the electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping). Under these conditions, ZnO NPs are chemically unstable due to their reaction with phosphates. The initial stage of transformation (around 5-10 h) involves the formation of a metastable solid (presumably ZnHPO4), which later evolves into the more stable hopeite phase. The overall decay rate of ZnO NPs is significantly reduced in comparison with phosphate-free background solutions of the same ionic strength and pH. The effective equilibrium solubilities of ZnO (0.29-0.47 mg.L-1), as well as conditional excess-ligand stability constants and fractional distributions of soluble Zn species, were determined in the absence and presence of organic components. The results were compared with the conventional ultrafiltration and inductively coupled plasma-mass spectrometry (UF-ICP-MS) methodology. AGNES proves to be advantageous in terms of speed, reproducibility, and access to speciation information. KeywordsThis work was supported by the Spanish Ministry MINECOunder Grant No. CTM2016-78798 and European UnionSeventh Framework Programme FP7-NMP.2012.1.3-3 underGrant No. 310584 (NANoREG). FQ gratefully acknowledgesa grant from AGAUR
Large-N Limit of Crossing Probabilities, Discontinuity, and Asymptotic Behavior of Threshold Values in Mandelbrot's Fractal Percolation Process
We study Mandelbrot's percolation process in dimension . The
process generates random fractal sets by an iterative procedure which starts by
dividing the unit cube in subcubes, and independently retaining
or discarding each subcube with probability or respectively. This
step is then repeated within the retained subcubes at all scales. As is
varied, there is a percolation phase transition in terms of paths for all , and in terms of -dimensional "sheets" for all .
For any , we consider the random fractal set produced at the
path-percolation critical value , and show that the probability that
it contains a path connecting two opposite faces of the cube tends to
one as . As an immediate consequence, we obtain that the above
probability has a discontinuity, as a function of , at for all
sufficiently large. This had previously been proved only for (for any
). For , we prove analogous results for sheet-percolation.
In dimension two, Chayes and Chayes proved that converges, as , to the critical density of site percolation on the square
lattice. Assuming the existence of the correlation length exponent for
site percolation on the square lattice, we establish the speed of convergence
up to a logarithmic factor. In particular, our results imply that
as , showing an
interesting relation with near-critical percolation.Comment: 24 pages, 2 figure
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