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The challenging binary production, diffusive pair contact process (PCPD)
Two absorbing states without symmetry, one of them is diffusive ( Carlon et al.(PRE 2001)). Numerical methods show new exponents, but are controversial. No extra symmetries or conservation laws found to explain it.
Bosonic field theories (1997) failed to describe critical behavior. In the bosonic model the active phase particle density diverges.
Fermionic model shows different critical behavior, but perturbative field theoretical renormalization did not find stable fixed point corresponding to the novel scaling behavior (2004). For a review see:
M. Henkel and H. Hinrichsen, J. Phys. A37, R117-R159 (2004)