1,071 research outputs found
Depinning exponents of the driven long-range elastic string
We perform a high-precision calculation of the critical exponents for the
long-range elastic string driven through quenched disorder at the depinning
transition, at zero temperature. Large-scale simulations are used to avoid
finite-size effects and to enable high precision. The roughness, growth, and
velocity exponents are calculated independently, and the dynamic and
correlation length exponents are derived. The critical exponents satisfy known
scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure
A Rapid Dynamical Monte Carlo Algorithm for Glassy Systems
In this paper we present a dynamical Monte Carlo algorithm which is
applicable to systems satisfying a clustering condition: during the dynamical
evolution the system is mostly trapped in deep local minima (as happens in
glasses, pinning problems etc.). We compare the algorithm to the usual Monte
Carlo algorithm, using as an example the Bernasconi model. In this model, a
straightforward implementation of the algorithm gives an improvement of several
orders of magnitude in computational speed with respect to a recent, already
very efficient, implementation of the algorithm of Bortz, Kalos and Lebowitz.Comment: RevTex 7 pages + 4 figures (uuencoded) appended; LPS preprin
Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation
After reviewing the concept of vison excitations in Z_2 dimer liquids, we
study the liquid-crystal transition of the Quantum Dimer Model on the
triangular lattice by means of a semiclassical spin-wave approximation to the
dispersion of visons in the context of a "soft-dimer" version of the model.
This approach captures some important qualitative features of the transition:
continuous nature of the transition, linear dispersion at the critical point,
and \sqrt{12}x\sqrt{12} symmetry-breaking pattern. In a second part, we present
a variational calculation of the vison dispersion relation at the RK point
which reproduces the qualitative shape of the dispersion relation and the order
of magnitude of the gap. This approach provides a simple but reliable
approximation of the vison wave functions at the RK point.Comment: 12 pages, 10 figures. v2: minor changes, to appear in Phys. Rev.
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
Event-chain Monte Carlo with factor fields
International audienceWe study the dynamics of one-dimensional (1D) interacting particles simulated with the event-chain Monte Carlo algorithm (ECMC). We argue that previous versions of the algorithm suffer from a mismatch in the factor potential between different particle pairs (factors) and show that in 1D models, this mismatch is overcome by factor fields. ECMC with factor fields is motivated, in 1D, for the harmonic model, and validated for the Lennard-Jones model as well as for hard spheres. In 1D particle systems with short-range interactions, autocorrelation times generally scale with the second power of the system size for reversible Monte Carlo dynamics, and with its first power for regular ECMC and for molecular-dynamics. We show, using numerical simulations, that they grow only with the square root of the systems size for ECMC with factor fields. Mixing times, which bound the time to reach equilibrium from an arbitrary initial configuration, grow with the first power of the system size
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
Hard-disk equation of state: First-order liquid-hexatic transition in two dimensions with three simulation methods
We report large-scale computer simulations of the hard-disk system at high
densities in the region of the melting transition. Our simulations reproduce
the equation of state, previously obtained using the event-chain Monte Carlo
algorithm, with a massively parallel implementation of the local Monte Carlo
method and with event-driven molecular dynamics. We analyze the relative
performance of these simulation methods to sample configuration space and
approach equilibrium. Our results confirm the first-order nature of the melting
phase transition in hard disks. Phase coexistence is visualized for individual
configurations via the orientational order parameter field. The analysis of
positional order confirms the existence of the hexatic phase.Comment: 9 pages, 8 figures, 2 table
Molecular simulation from modern statistics: Continuous-time, continuous-space, exact
In a world made of atoms, the computer simulation of molecular systems, such
as proteins in water, plays an enormous role in science. Software packages that
perform these computations have been developed for decades. In molecular
simulation, Newton's equations of motion are discretized and long-range
potentials are treated through cutoffs or spacial discretization, which all
introduce approximations and artifacts that must be controlled algorithmically.
Here, we introduce a paradigm for molecular simulation that is based on modern
concepts in statistics and is rigorously free of discretizations,
approximations, and cutoffs. Our demonstration software reaches a break-even
point with traditional molecular simulation at high precision. We stress the
promise of our paradigm as a gold standard for critical applications and as a
future competitive approach to molecular simulation.Comment: 19 pages, 4 figures; 18 pages supplementary materials, 1
supplementary figur
Coexistence of solutions in dynamical mean-field theory of the Mott transition
In this paper, I discuss the finite-temperature metal-insulator transition of
the paramagnetic Hubbard model within dynamical mean-field theory. I show that
coexisting solutions, the hallmark of such a transition, can be obtained in a
consistent way both from Quantum Monte Carlo (QMC) simulations and from the
Exact Diagonalization method. I pay special attention to discretization errors
within QMC. These errors explain why it is difficult to obtain the solutions by
QMC close to the boundaries of the coexistence region.Comment: 3 pages, 2 figures, RevTe
- …