Universality of continuous and discrete conserved Manna models in one dimension

The critical behaviour of an absorbing phase transition for the conserved continuous Manna model (CCMM) was investigated in one dimension via extensive Monte Carlo simulations, using sequential updates from the uniform initial states. The discrete conserved Manna model (DCMM) was also revisited and previous data, together with newly generated data, were reanalysed and compared with those for the CCMM. All critical exponents in the two models appear to be consistent to within statistical error, whereas the off-critical scaling function takes a different form in each model. The results differed by less than 10% from those of the directed percolation (DP) universality class. To examine the existence of the Griffith phase, additional simulations were carried out on a stripe of 105×20 lattice sites, 20% of which were diluted. While the non-universal power laws were reported for the models in the DP class, there was no sign of the Griffith phase in either model. Thus, we conclude that both the DCMM and CCMM belong to a universality class that is different from the DP class. We examine the possibility of weak universality between the discrete and continuous models, whereby the critical exponents are similar, but the off-critical scaling functions are different.