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