Double transitions, non-Ising criticality and the critical absorbing phase in an interacting monomer?dimer model on a square lattice

We present a numerical study on an interacting monomer–dimer model with nearest neighbor repulsion on a square lattice, which possesses two symmetric absorbing states. The model is observed to exhibit two nearby continuous transitions: the Z2 symmetry-breaking order–disorder transition and the absorbing transition with directed percolation criticality. We find that the symmetry-breaking transition shows a non-Ising critical behavior, and that the absorbing phase becomes critical, in the sense that the critical decay of the dimer density observed at the absorbing transition persists even within the absorbing phase. Our findings call for further studies on microscopic models and the corresponding continuum description belonging to the generalized voter university class.