An apparent violation of hyperscaling at the endpoint of the critical line in the Domany-Kinzel stochastic cellular automaton finds an elementary resolution upon noting that the order parameter is discontinuous at this point. We derive a hyperscaling relation for such transitions and discuss applications to related examples.

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We introduce a parity conserving version of the contact process, which can be treated using a series expansion technique. Both Padé approximants for the series and numerical simulations for the derivative of the order parameter show that the critical exponent b is consistent with the conjecture b 1. Dynamical Monte Carlo simulations confirm that the model belongs to the branching annihilating random walk with an even number of offsprings universality class. [S0031-9007 (98)06309-1] PACS numbers: 64.60.Ak, 05.40. + j, 64.60.Ht Contact process (CP) [1,2] is a nonequilibrium model exhibiting an extinction-survival second order dynamical phase transition. The basic CP introduced by Harris [1]has a unique absorbing state and belongs to the directed percolation (DP) universality class [3][4][5]. Many other nonequilibrium models such as A-model [6,7], branching annihilating random walk [8,9] with an odd number of offsprings, and Reggon field theory [10] are believed to belong to the same universality class as the basic contact process, which is often regarded as a minimal example of a broad class of interacting particle systems, similarly to the role of the Ising system in equilibrium critical phenomena.Another important universality class for nonequilibrium models is branching annihilating random walk with even offsprings universality class (BAWe) [11,12]. The first model belonging to a non-DP, and now believed to belong to the BAWe universality class was a probabilistic cellular automaton studied by Grassbeger et al. [13]. Recently, a number of models belonging to BAWe universality, such as certain kinetic Ising models [14], the interacting monomer-dimer model (MDM) [15,16], three species monomer-monomer model [17], and modified DomanyKinzel model [18] introduced by Hinrichsen [19] attracted much attention. While for DP universality models series expansion treatment proved to be most effective in estimating critical values (see references above), so far models in BAWe universality relied exclusively on Monte Carlo simulations.Although the DP universality class is very wide and includes models with rather simple rules, no model in it has been solved exactly [20]. Guttmann and Enting [21] suggested that DP models will never be solved exactly in the sense of being expressed in terms of D-finite functions due to an absence of pattern in series expansion coefficients. Furthermore, based on numerical data Jensen and Guttmann [5] conjectured that critical exponents for DP should not be expected to be simple rational fractions.On the other hand, Jensen conjectured that combinations of critical exponents of BAWe can be represented as b͞n Ќ 1 2 and n Ќ ͞n k 7͞4 [11]. Intuitively, it would suggest that BAWe universality is "simpler" than DP universality; one could even speculate concerning the possibility of an exact solution.In this Letter, we introduce a extended CP, which while belonging to BAWe universality allows a series expansion treatment. We use the series expansion technique [22][23][24] in order to clarify the value o...

We study mixed site-bond directed percolation on 2D and 3D lattices by using time-dependent simulations. Our results are compared with rigorous bounds recently obtained by Liggett and by Katori and Tsukahara.The critical fractions p c site and p c bond of sites and bonds are extremely well approximated by a relationship reported earlier for isotropic percolation,

We study the percolation properties of a random diode network (RDN) which contains two kinds of directed bonds on a square lattice. This network is a special case of the random insulation-resistor-diode network. Both Monte Carlo simulations and series expansion for the percolation probability show that an estimated critical exponent, beta=0.1794+/-0.008, is different from known values for a conventional insulation-resistor-diode network. RDN belongs to neither the isotropic percolation universality class nor to the directed percolation universality, which we attribute to a difference of symmetry breakdown around the critical point.