On possible experimental realizations of directed percolation

Directed percolation is one of the most prominent universality classes of nonequilibrium phase transitions and can be found in a large variety of models. Despite its theoretical success, no experiment is known which clearly reproduces the critical exponents of directed percolation. The present work compares suggested experiments and discusses possible reasons why the observation of the critical exponents of directed percolation is obscured or even impossible.Comment: RevTeX, 13 pages, 11 eps figure

Roughening transition driven by a binary spreading process

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A->3A, 2A->0.Comment: RevTeX, 6 pages, 6 eps figure

The Pokrovski-Talapov Phase Transitions and Quantum Groups

We show that the XY quantum chain in a magnetic field is invariant under a two parameter deformation of the $SU(1/1)$ superalgebra. One is led to an extension of the braid group and the Hecke algebras which reduce to the known ones when the two parameter coincide. The physical significance of the two parameters is discussed. When both are equal to one, one gets a Pokrovski-Talapov phase transition. We also show that the representation theory of the quantum superalgebras indicates how to take the appropriate thermodynamical limits.Comment: 9 page

A model for anomalous directed percolation

We introduce a model for the spreading of epidemics by long-range infections and investigate the critical behaviour at the spreading transition. The model generalizes directed bond percolation and is characterized by a probability distribution for long-range infections which decays in $d$ spatial dimensions as $1/r^{d+\sigma}$. Extensive numerical simulations are performed in order to determine the density exponent $\beta$ and the correlation length exponents $\nu_{||}$ and $\nu_\perp$ for various values of $\sigma$. We observe that these exponents vary continuously with $\sigma$, in agreement with recent field-theoretic predictions. We also study a model for pairwise annihilation of particles with algebraically distributed long-range interactions.Comment: RevTeX, 9 pages, including 6 eps-figure