Ordering and percolation transitions for hard squares: Equilibrium versus nonequilibrium models for adsorbed layers with c(2x2) superlattice ordering

We study the critical behavior of models for adsorbed layers in which parti cles reside on a square lattice and have infinite nearest-neighbor repulsio ns. Such particles are often described as "hard squares." We consider both the equilibrium hard-square model and a nonequilibrium model. The latter in volves dimer adsorption onto diagonally adjacent sites, and the desorption and possible hopping of adsorbed monomer particles (where neither adsorptio n nor hopping can create adjacent pairs of occupied sites). In the limit or high monomer mobility, one recovers the equilibrium model. Both models exh ibit a continuous symmetry breaking transition in the Ising universality cl ass, and also a percolation transition for c(2x2) clusters of particles con nected with diagonal bonds. For the equilibrium model, extensive Monte Carl o simulations show that the two transitions coincide, supporting the claim of Hu and Mak. We also determine percolation exponents for c(2x2) clusters and vacancy clusters, and consider a correlated site-bond percolation probl em which elucidates conditions for coincidence of symmetry-breaking and per colation. In contrast, for the nonequilibrium model with immobile adsorbed monomers, there is a gap between the symmetry-breaking and percolation tran sitions, and the random percolation universality class applies. Finally, we examine the crossover behavior with increasing mobility of adsorbed monome rs.