Scaling Relations in Absorbing Phase Transitions with a Conserved Field in One Dimension

Validity of two scaling relations β = ν ∥ θ and z = ν ∥ / ν ⊥ widely known in absorbing phase transitions is studied for the conserved lattice gas (CLG) model and the conserved threshold transfer process CTTP) both in one dimension. For the CLG model, it is found that both relations hold when the critical exponents calculated from the all-sample average density of active particles are considered. For the CTTP model, various exponents are calculated via Monte Carlo simulations and they are confirmed by the off-critical scaling and the finite-size scaling analyses. The exponents estimated from the all-sample averages again satisfy both relations. These observations are in strict disagreement with earlier observations in two dimensions [Phys. Rev. Lett. 85, 1803 (2000); Phys Rev. E 68, 056102 (2003)] but support the more recent observation for the CLG model [Phys. Rev. E 78, 040103(R) (2008)].