Death by mutants: unusual multicritical dynamics in a two-species model for absorbing state transitions

We explore the phases and active-to-absorbing state phase transitions (AAPT) in a two-species model, where the species A and its mutant B are {\em asymmetrically} or {\em nonreciprocally} coupled. We identify a multicritical point that connects the global absorbing state of both the species and its mutant, with a uniform active state. The critical dynamics at this multicritical point is studied within the lowest order perturbation theory. This asymmetric coupling between species A and mutant B leads to unequal and distinct upper critical dimensions $d_c^A$ and $d_c^B$ respectively for A and B dynamics. We show that the multicritical point in this model is characterised by an unusual breakdown of scale-invariance by fluctuation-induced logarithmic modulations with power law behaviour of the order parameter and correlation lengths of the species A at all dimensions $d<d_c^A$. Above $d_c^A$, conventional scale-invariance is restored. The dynamics of the mutant species B belongs to the DP universality class with an upper critical dimension of $d_c^B=4$