Crossover from the pair contact process with diffusion to directed percolation

Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation/branching dynamics. The crossover exponents $\phi$ are estimated numerically as $1/\phi \simeq 0.58\pm0.03$ for the PCPD and $1/\phi \simeq 0.49 \pm 0.02$ for the DPCPD. Nontriviality of the PCPD crossover exponent strongly supports non-DP nature of the PCPD critical scaling, which is further evidenced by the anomalous critical amplitude scaling near the PCPD point. In addition, we find that the DPCPD crossover is consistent with the mean field prediction of the tricritical DP class as expected

Crossover from the parity-conserving pair contact process with diffusion to other universality classes

The pair contact process with diffusion (PCPD) with modulo 2 conservation (\pcpdt) [$2A\to 4A$, $2A\to 0$] is studied in one dimension, focused on the crossover to other well established universality classes: the directed Ising (DI) and the directed percolation (DP). First, we show that the \pcpdt shares the critical behaviors with the PCPD, both with and without directional bias. Second, the crossover from the \pcpdt to the DI is studied by including a parity-conserving single-particle process ($A \to 3A$). We find the crossover exponent $1/\phi_1 = 0.57(3)$, which is argued to be identical to that of the PCPD-to-DP crossover by adding $A \to 2A$. This suggests that the PCPD universality class has a well defined fixed point distinct from the DP. Third, we study the crossover from a hybrid-type reaction-diffusion process belonging to the DP [$3A\to 5A$, $2A\to 0$] to the DI by adding $A \to 3A$. We find $1/\phi_2 = 0.73(4)$ for the DP-to-DI crossover. The inequality of $\phi_1$ and $\phi_2$ further supports the non-DP nature of the PCPD scaling. Finally, we introduce a symmetry-breaking field in the dual spin language to study the crossover from the \pcpdt to the DP. We find $1/\phi_3 = 1.23(10)$, which is associated with a new independent route from the PCPD to the DP.Comment: 8 pages, 8 figure

Remark on the effective potential of the gravitational perturbation in the black hole background projected on the brane

The polar perturbation is examined when the spacetime is expressed by a 4d metric induced from higher-dimensional Schwarzschild geometry. Since the spacetime background is not a vacuum solution of 4d Einstein equation, the various general principles are used to understand the behavior of the energy-momentum tensor under the perturbation. It is found that although the general principles fix many components, they cannot fix two components of the energy-momentum tensor. Choosing two components suitably, we derive the effective potential which has a correct 4d limit.Comment: 12 pages, no figure, CQG accepte