Driven Pair Contact Process with Diffusion
  The pair contact process with diffusion (PCPD) has been recently investigated extensively, but its critical behavior is not yet clearly established. By introducing biased diffusion, we show that the external driving is relevant and the driven PCPD exhibits a mean-field-type critical behavior even in one dimension. In systems which can be described by a single-species bosonic field theory, the Galilean invariance guarantees that the driving is irrelevant. The well-established directed percolation (DP) and parity conserving (PC) classes are such examples. This leads us to conclude that the PCPD universality class should be distinct from the DP or PC class. Moreover, it implies that the PCPD is generically a multi-species model and a field theory of two species is suitable for proper description. 
Su-Chan Park and Hyunggyu Park