2,794 research outputs found
Elasticity of a contact-line and avalanche-size distribution at depinning
Motivated by recent experiments, we extend the Joanny-deGennes calculation of
the elasticity of a contact line to an arbitrary contact angle and an arbitrary
plate inclination in presence of gravity. This requires a diagonalization of
the elastic modes around the non-linear equilibrium profile, which is carried
out exactly. We then make detailed predictions for the avalanche-size
distribution at quasi-static depinning: we study how the universal (i.e.
short-scale independent) rescaled size distribution and the ratio of moments of
local to global avalanches depend on the precise form of the elastic kernel.Comment: 15 pages, 11 figure
Meron-Cluster Solution of Fermion and Other Sign Problems
Numerical simulations of numerous quantum systems suffer from the notorious
sign problem. Important examples include QCD and other field theories at
non-zero chemical potential, at non-zero vacuum angle, or with an odd number of
flavors, as well as the Hubbard model for high-temperature superconductivity
and quantum antiferromagnets in an external magnetic field. In all these cases
standard simulation algorithms require an exponentially large statistics in
large space-time volumes and are thus impossible to use in practice.
Meron-cluster algorithms realize a general strategy to solve severe sign
problems but must be constructed for each individual case. They lead to a
complete solution of the sign problem in several of the above cases.Comment: 15 pages,LATTICE9
The Center symmetry and its spontaneous breakdown at high temperatures
We examine the role of the center Z(N) of the gauge group SU(N) in gauge
theories. In this pedagogical article, we discuss, among other topics, the
center symmetry and confinement and deconfinement in gauge theories and
associated finite-temperature phase transitions. We also look at universal
properties of domain walls separating distinct confined and deconfined bulk
phases, including a description of how QCD color-flux strings can end on
color-neutral domain walls, and unusual finite-volume dependence in which
quarks in deconfined bulk phase seem to be "confined".Comment: LaTex, 35 pages, 6 figures, uses sprocl.sty. To be published in the
Festschrift in honor of B.L. Ioffe, "At the Frontier of Particle Physics/
Handbook of QCD", edited by M. Shifma
Meron-Cluster Simulation of a Chiral Phase Transition with Staggered Fermions
We examine a (3+1)-dimensional model of staggered lattice fermions with a
four-fermion interaction and Z(2) chiral symmetry using the Hamiltonian
formulation. This model cannot be simulated with standard fermion algorithms
because those suffer from a very severe sign problem. We use a new fermion
simulation technique - the meron-cluster algorithm - which solves the sign
problem and leads to high-precision numerical data. We investigate the finite
temperature chiral phase transition and verify that it is in the universality
class of the 3-d Ising model using finite-size scaling.Comment: 21 pages, 6 figure
Distribution of velocities in an avalanche
For a driven elastic object near depinning, we derive from first principles
the distribution of instantaneous velocities in an avalanche. We prove that
above the upper critical dimension, d >= d_uc, the n-times distribution of the
center-of-mass velocity is equivalent to the prediction from the ABBM
stochastic equation. Our method allows to compute space and time dependence
from an instanton equation. We extend the calculation beyond mean field, to
lowest order in epsilon=d_uc-d.Comment: 4 pages, 2 figure
Size distributions of shocks and static avalanches from the Functional Renormalization Group
Interfaces pinned by quenched disorder are often used to model jerky
self-organized critical motion. We study static avalanches, or shocks, defined
here as jumps between distinct global minima upon changing an external field.
We show how the full statistics of these jumps is encoded in the
functional-renormalization-group fixed-point functions. This allows us to
obtain the size distribution P(S) of static avalanches in an expansion in the
internal dimension d of the interface. Near and above d=4 this yields the
mean-field distribution P(S) ~ S^(-3/2) exp(-S/[4 S_m]) where S_m is a
large-scale cutoff, in some cases calculable. Resumming all 1-loop
contributions, we find P(S) ~ S^(-tau) exp(C (S/S_m)^(1/2) -B/4 (S/S_m)^delta)
where B, C, delta, tau are obtained to first order in epsilon=4-d. Our result
is consistent to O(epsilon) with the relation tau = 2-2/(d+zeta), where zeta is
the static roughness exponent, often conjectured to hold at depinning. Our
calculation applies to all static universality classes, including random-bond,
random-field and random-periodic disorder. Extended to long-range elastic
systems, it yields a different size distribution for the case of contact-line
elasticity, with an exponent compatible with tau=2-1/(d+zeta) to
O(epsilon=2-d). We discuss consequences for avalanches at depinning and for
sandpile models, relations to Burgers turbulence and the possibility that the
above relations for tau be violated to higher loop order. Finally, we show that
the avalanche-size distribution on a hyper-plane of co-dimension one is in
mean-field (valid close to and above d=4) given by P(S) ~ K_{1/3}(S)/S, where K
is the Bessel-K function, thus tau=4/3 for the hyper plane.Comment: 34 pages, 30 figure
Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
We have measured the center-of-mass fluctuations of the height of a contact
line at depinning for two different systems: liquid hydrogen on a rough cesium
substrate and isopropanol on a silicon wafer grafted with silanized patches.
The contact line is subject to a confining quadratic well, provided by gravity.
From the second cumulant of the height fluctuations, we measure the
renormalized disorder correlator Delta(u), predicted by the Functional RG
theory to attain a fixed point, as soon as the capillary length is large
compared to the Larkin length set by the microscopic disorder. The experiments
are consistent with the asymptotic form for Delta(u) predicted by Functional
RG, including a linear cusp at u=0. The observed small deviations could be used
as a probe of the underlying physical processes. The third moment, as well as
avalanche-size distributions are measured and compared to predictions from
Functional RG.Comment: 6 pages, 14 figure
When is the deconfinement phase transition universal?
Pure Yang-Mills theory has a finite-temperature phase transition, separating
the confined and deconfined bulk phases. Svetitsky and Yaffe conjectured that
if this phase transition is of second order, it belongs to the universality
class of transitions for particular scalar field theories in one lower
dimension. We examine Yang-Mills theory with the symplectic gauge groups Sp(N).
We find new evidence supporting the Svetitsky-Yaffe conjecture and make our own
conjecture as to which gauge theories have a universal second order
deconfinement phase transition.Comment: 5 pages, 4 figures; Contribution to Confinement 2003, Tokyo, Japan,
July 21-24, 200
Meron-cluster algorithms and chiral symmetry breaking in a (2+1)-d staggered fermion model
The recently developed Meron-Cluster algorithm completely solves the
exponentially difficult sign problem for a number of models previously
inaccessible to numerical simulation. We use this algorithm in a high-precision
study of a model of N=1 flavor of staggered fermions in (2+1)-dimensions with a
four-fermion interaction. This model cannot be explored using standard
algorithms. We find that the Z(2) chiral symmetry of this model is
spontaneously broken at low temperatures and that the finite-temperature chiral
phase transition is in the universality class of the 2-d Ising model, as
expected.Comment: 18 pages, LaTe
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