1,102 research outputs found
Vacancy diffusion in the triangular lattice dimer model
We study vacancy diffusion on the classical triangular lattice dimer model,
sub ject to the kinetic constraint that dimers can only translate, but not
rotate. A single vacancy, i.e. a monomer, in an otherwise fully packed lattice,
is always localized in a tree-like structure. The distribution of tree sizes is
asymptotically exponential and has an average of 8.16 \pm 0.01 sites. A
connected pair of monomers has a finite probability of being delocalized. When
delocalized, the diffusion of monomers is anomalous:Comment: 15 pages, 27 eps figures. submitted to Physical Review
Selective-pivot sampling of radial distribution functions in asymmetric liquid mixtures
We present a Monte Carlo algorithm for selectively sampling radial
distribution functions and effective interaction potentials in asymmetric
liquid mixtures. We demonstrate its efficiency for hard-sphere mixtures, and
for model systems with more general interactions, and compare our simulations
with several analytical approximations. For interaction potentials containing a
hard-sphere contribution, the algorithm yields the contact value of the radial
distribution function.Comment: 5 pages, 5 figure
Off-diagonal long-range order, cycle probabilities, and condensate fraction in the ideal Bose gas
We discuss the relationship between the cycle probabilities in the
path-integral representation of the ideal Bose gas, off-diagonal long-range
order, and Bose--Einstein condensation. Starting from the Landsberg recursion
relation for the canonic partition function, we use elementary considerations
to show that in a box of size L^3 the sum of the cycle probabilities of length
k >> L^2 equals the off-diagonal long-range order parameter in the
thermodynamic limit. For arbitrary systems of ideal bosons, the integer
derivative of the cycle probabilities is related to the probability of
condensing k bosons. We use this relation to derive the precise form of the
\pi_k in the thermodynamic limit. We also determine the function \pi_k for
arbitrary systems. Furthermore we use the cycle probabilities to compute the
probability distribution of the maximum-length cycles both at T=0, where the
ideal Bose gas reduces to the study of random permutations, and at finite
temperature. We close with comments on the cycle probabilities in interacting
Bose gases.Comment: 6 pages, extensive rewriting, new section on maximum-length cycle
Eigenvalue Distributions in Yang-Mills Integrals
We investigate one-matrix correlation functions for finite SU(N) Yang-Mills integrals with and without supersymmetry. We propose novel convergence conditions for these correlators which we determine from the one-loop perturbative effective action. These conditions are found to agree with non-perturbative Monte Carlo calculations for various gauge groups and dimensions. Our results yield important insights into the eigenvalue distributions rho(lambda) of these random matrix models. For the bosonic models, we find that the spectral densities rho(lambda) possess moments of all orders as N -> Infinity. In the supersymmetric case, rho(lambda) is a wide distribution with an N-independent asymptotic behavior rho(lambda) ~ lambda^(-3), lambda^(-7), lambda^(-15) for dimensions D=4,6,10, respectively
Critical Current Peaks at in Superconductors with Columnar Defects: Recrystalizing the Interstitial Glass
The role of commensurability and the interplay of correlated disorder and
interactions on vortex dynamics in the presence of columnar pins is studied via
molecular dynamics simulations. Simulations of dynamics reveal substantial
caging effects and a non-monotonic dependence of the critical current with
enhancements near integer values of the matching field and
in agreement with experiments on the cuprates. We find qualitative
differences in the phase diagram for small and large values of the matching
field.Comment: 5 pages, 4 figures (3 color
Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?
The motion of driven interfaces in random media at finite temperature and
small external force is usually described by a linear displacement at large times, where the velocity vanishes according to the
creep formula as for . In this paper,
we question this picture on the specific example of the directed polymer in a
two dimensional random medium. We have recently shown (C. Monthus and T. Garel,
arxiv:0802.2502) that its dynamics for F=0 can be analyzed in terms of a strong
disorder renormalization procedure, where the distribution of renormalized
barriers flows towards some "infinite disorder fixed point". In the present
paper, we obtain that for small , this "infinite disorder fixed point"
becomes a "strong disorder fixed point" with an exponential distribution of
renormalized barriers. The corresponding distribution of trapping times then
only decays as a power-law , where the exponent
vanishes as as . Our
conclusion is that in the small force region , the divergence of
the averaged trapping time induces strong
non-self-averaging effects that invalidate the usual creep formula obtained by
replacing all trapping times by the typical value. We find instead that the
motion is only sub-linearly in time , i.e. the
asymptotic velocity vanishes V=0. This analysis is confirmed by numerical
simulations of a directed polymer with a metric constraint driven in a traps
landscape. We moreover obtain that the roughness exponent, which is governed by
the equilibrium value up to some large scale, becomes equal to
at the largest scales.Comment: v3=final versio
Statistical mechanics of lossy compression using multilayer perceptrons
Statistical mechanics is applied to lossy compression using multilayer
perceptrons for unbiased Boolean messages. We utilize a tree-like committee
machine (committee tree) and tree-like parity machine (parity tree) whose
transfer functions are monotonic. For compression using committee tree, a lower
bound of achievable distortion becomes small as the number of hidden units K
increases. However, it cannot reach the Shannon bound even where K -> infty.
For a compression using a parity tree with K >= 2 hidden units, the rate
distortion function, which is known as the theoretical limit for compression,
is derived where the code length becomes infinity.Comment: 12 pages, 5 figure
Adding a Myers Term to the IIB Matrix Model
We show that Yang-Mills matrix integrals remain convergent when a Myers term
is added, and stay in the same topological class as the original model. It is
possible to add a supersymmetric Myers term and this leaves the partition
function invariant.Comment: 8 pages, v2 2 refs adde
Mean properties and Free Energy of a few hard spheres confined in a spherical cavity
We use analytical calculations and event-driven molecular dynamics
simulations to study a small number of hard sphere particles in a spherical
cavity. The cavity is taken also as the thermal bath so that the system
thermalizes by collisions with the wall. In that way, these systems of two,
three and four particles, are considered in the canonical ensemble. We
characterize various mean and thermal properties for a wide range of number
densities. We study the density profiles, the components of the local pressure
tensor, the interface tension, and the adsorption at the wall. This spans from
the ideal gas limit at low densities to the high-packing limit in which there
are significant regions of the cavity for which the particles have no access,
due the conjunction of excluded volume and confinement. The contact density and
the pressure on the wall are obtained by simulations and compared to exact
analytical results. We also obtain the excess free energy for N=4, by using a
simulated-assisted approach in which we combine simulation results with the
knowledge of the exact partition function for two and three particles in a
spherical cavity.Comment: 11 pages, 9 figures and two table
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