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When this reaction is absent the model is soluble but this solution does not help understanding the phase transition we study here, see, J. Phys. A: Math. Gen. J. Phys. A: Math. Gen, vol.30, issue.37, p.4709, 1997. ,
the RG flow goes towards the Gaussian fixed point at small initial coupling for d > 2 [29] (the interface is flat), while at large coupling it goes towards a strong coupling fixed point (the interface is rough) [4, 30] and for d < 2 the interface is always rough. Two is thus the critical dimension at small coupling as in PCPD ,