Logarithmic roughening in a growth process with edge evaporation

Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [Phys. Rev. Lett. 76, 2746 (1996)], where the interface is known to roughen logarithmically with time. Performing high-precision simulations we find appropriate scaling forms for various quantities. Moreover we present a simple approximation explaining why the interface roughens logarithmically.Comment: revtex, 6 pages, 7 eps figure

Equal-time correlation function for directed percolation

We suggest an equal-time n-point correlation function for systems in the directed percolation universality class which is well defined in all phases and independent of initial conditions. It is defined as the probability that all points are connected with a common ancestor in the past by directed paths.Comment: LaTeX, 12 pages, 8 eps figure

Boundary-induced nonequilibrium phase transition into an absorbing state

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.Comment: 4 pages, 4 figures; minor change

Binary spreading process with parity conservation

Recently there has been a debate concerning the universal properties of the phase transition in the pair contact process with diffusion (PCPD) $2A\to 3A, 2A\to \emptyset$. Although some of the critical exponents seem to coincide with those of the so-called parity-conserving universality class, it was suggested that the PCPD might represent an independent class of phase transitions. This point of view is motivated by the argument that the PCPD does not conserve parity of the particle number. In the present work we pose the question what happens if the parity conservation law is restored. To this end we consider the the reaction-diffusion process $2A\to 4A, 2A\to \emptyset$. Surprisingly this process displays the same type of critical behavior, leading to the conclusion that the most important characteristics of the PCPD is the use of binary reactions for spreading, regardless of whether parity is conserved or not.Comment: RevTex, 4pages, 4 eps figure

Epidemic spreading with immunization and mutations

The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies out. In nature, however, the transmitted pathogen may also mutate, weakening the effect of immunization. In order to study the influence of mutations, we introduce a model that mimics epidemic spreading with immunization and mutations. The model exhibits a line of continuous phase transitions and includes the general epidemic process (GEP) and directed percolation (DP) as special cases. Restricting to perfect immunization in two spatial dimensions we analyze the phase diagram and study the scaling behavior along the phase transition line as well as in the vicinity of the GEP point. We show that mutations lead generically to a crossover from the GEP to DP. Using standard scaling arguments we also predict the form of the phase transition line close to the GEP point. It turns out that the protection gained by immunization is vitally decreased by the occurrence of mutations.Comment: 9 pages, 13 figure

Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics

A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble, where the total number of the particles is being fixed, we find that the model has a rather non-trivial phase diagram consisting of three different phases which are separated by second-order phase transition. Shocks may evolve in the system for special values of the reaction parameters.Comment: 8 pages, 3 figure

Absorbing Phase Transitions of Branching-Annihilating Random Walks

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of non-trivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.Comment: 4 pages, 4 figure

Five-dimensional Superfield Supergravity

We present a projective superspace formulation for matter-coupled simple supergravity in five dimensions. Our starting point is the superspace realization for the minimal supergravity multiplet proposed by Howe in 1981. We introduce various off-shell supermultiplets (i.e. hypermultiplets, tensor and vector multiplets) that describe matter fields coupled to supergravity. A projective-invariant action principle is given, and specific dynamical systems are constructed including supersymmetric nonlinear sigma-models. We believe that this approach can be extended to other supergravity theories with eight supercharges in $D\leq 6$ space-time dimensions, including the important case of 4D N=2 supergravity.Comment: 18 pages, LaTeX; v2: comments added; v3: minor changes, references added; v4: comments, reference added, version to appear in PL