Finite-size scaling of directed percolation above the upper critical dimension.

We consider analytically as well as numerically the finite-size scaling behavior in the stationary state near the nonequilibrium phase transition of directed percolation within the mean field regime, i.e., above the upper critical dimension. Analogous to equilibrium, usual finite-size scaling is valid below the upper critical dimension, whereas it fails above. Performing a momentum analysis of associated path integrals we derive modified finite-size scaling forms of the order parameter and its higher moments. The results are confirmed by numerical simulations of corresponding high-dimensional lattice models.

Random resistor-diode networks and the crossover from isotropic to directed percolation

By employing the methods of renormalized field theory, we show that the percolation behavior of random resistor-diode networks near the multicritical line belongs to the universality class of isotropic percolation. We construct a mesoscopic model from the general epidemic process by including a relevant isotropy-breaking perturbation. We present a two-loop calculation of the crossover exponent straight phi. Upon blending the varepsilon-expansion result with the exact value straight phi=1 for one dimension by a rational approximation, we obtain straight phi=1.29+/-0.05 for two dimensions. This value is in agreement with the recent simulations of a two-dimensional random diode network by Inui, et al. [Phys. Rev. E 59, 6513 (1999)], who found an order parameter exponent beta different from those of isotropic and directed percolation. Furthermore, we reconsider the theory of the full crossover from isotropic to directed percolation by Frey, Tauber, and Schwabl [Europhys. Lett. 26, 413 (1994); Phys. Rev. E 49, 5058 (1994)], and clear up some minor shortcomings.

Viability of competing field theories for the driven lattice gas

It has recently been suggested that the driven lattice gas should be described by an alternate field theory in the limit of infinite drive. We review the original and the alternate field theory, invoking several well-documented key features of the microscopics. Since the alternate field theory fails to reproduce these characteristics, we argue that it cannot serve as a viable description of the driven lattice gas. Recent results, for the critical exponents associated with this theory, are reanalyzed and shown to be incorrect.