Correlations of a bound interface over a random substrate

The correlation function of a one-dimensional interface over a random substrate, bound to the substrate by a pressure term, is studied by Monte-Carlo simulation. It is found that the height correlation , averaged over the substrate disorder, fits a form exp(-(j/b)^c) to a surprising precision in the full range of j where the correlation is non-negligible. The exponent c increases from 1.0 to 1.5 when the interface tension is taken larger and larger.Comment: 7 pages, 5 figure

A Note on Edwards' Hypothesis for Zero-Temperature Ising Dynamics

We give a simple criterion for checking the so called Edwards' hypothesis in certain zero-temperature, ferromagnetic spin-flip dynamics and use it to invalidate the hypothesis in various examples in dimension one and higher.Comment: 11 pages, 4 figure

Potts-Percolation-Gauss Model of a Solid

We study a statistical mechanics model of a solid. Neighboring atoms are connected by Hookian springs. If the energy is larger than a threshold the "spring" is more likely to fail, while if the energy is lower than the threshold the spring is more likely to be alive. The phase diagram and thermodynamic quantities, such as free energy, numbers of bonds and clusters, and their fluctuations, are determined using renormalization-group and Monte-Carlo techniques.Comment: 10 pages, 12 figure

Percolation on the average and spontaneous magnetization for q-states Potts model on graph

We prove that the q-states Potts model on graph is spontaneously magnetized at finite temperature if and only if the graph presents percolation on the average. Percolation on the average is a combinatorial problem defined by averaging over all the sites of the graph the probability of belonging to a cluster of a given size. In the paper we obtain an inequality between this average probability and the average magnetization, which is a typical extensive function describing the thermodynamic behaviour of the model

Stretched exponential relaxation for growing interfaces in quenched disordered media

We study the relaxation for growing interfaces in quenched disordered media. We use a directed percolation depinning model introduced by Tang and Leschhorn for 1+1-dimensions. We define the two-time autocorrelation function of the interface height C(t',t) and its Fourier transform. These functions depend on the difference of times t-t' for long enough times, this is the steady-state regime. We find a two-step relaxation decay in this regime. The long time tail can be fitted by a stretched exponential relaxation function. The relaxation time is proportional to the characteristic distance of the clusters of pinning cells in the direction parallel to the interface and it diverges as a power law. The two-step relaxation is lost at a given wave length of the Fourier transform, which is proportional to the characteristic distance of the clusters of pinning cells in the direction perpendicular to the interface. The stretched exponential relaxation is caused by the existence of clusters of pinning cells and it is a direct consequence of the quenched noise.Comment: 4 pages and 5 figures. Submitted (5/2002) to Phys. Rev.

The Thermodynamics of Quarks and Gluons

This is an introduction to the study of strongly interacting matter. We survey its different possible states and discuss the transition from hadronic matter to a plasma of deconfined quarks and gluons. Following this, we summarize the results provided by lattice QCD finite temperature and density, and then investigate the nature of the deconfinement transition. Finally we give a schematic overview of possible ways to study the properties of the quark-gluon plasma.Comment: 19 pages, 21 figures; lecture given at the QGP Winter School, Jaipur/India, Feb.1-3, 2008; to appear in Springer Lecture Notes in Physic

Thermal Operators in Ising Percolation

We discuss a new cluster representation for the internal energy and the specific heat of the d-dimensional Ising model, obtained by studying the percolation mapping of an Ising model with an arbitrary set of antiferromagnetic links. Such a representation relates the thermal operators to the topological properties of the Fortuin-Kasteleyn clusters of Ising percolation and is a powerful tool to get new exact relations on the topological structure of FK clusters of the Ising model defined on an arbitrary graph.Comment: 17 pages, 2 figures. Improved version. Major changes in the text and in the notations. A missing term added in the specific heat representatio

Monopole clusters, center vortices, and confinement in a Z(2) gauge-Higgs system

We propose to use the different kinds of vacua of the gauge theories coupled to matter as a laboratory to test confinement ideas of pure Yang-Mills theories. In particular, the very poor overlap of the Wilson loop with the broken string states supports the 't Hooft and Mandelstam confinement criteria. However in the Z(2) gauge-Higgs model we use as a guide we find that the condensation of monopoles and center vortices is a necessary, but not sufficient condition for confinement.Comment: 13 pages, 6 figures, minor changes, version to be published on Phys. Rev.