Static critical behavior in the inactive phase of the pair contact process

Steady-state properties in the absorbing phase of the $1d$ pair contact process model are investigated. It is shown that, in typical absorbing states (reached by the system’s dynamic rules), the density of isolated particles ${\rho }_1,$ approaches a stationary value that depends on the annihilation probability $\mathrm{}\left(p\right);$ the deviation from its “natural” value at criticality ${\rho }_1^{\mathrm{nat}}$ follows a power law: ${\rho }_1^{\mathrm{nat}}-{\rho }_1\sim (p-p_c{)}^{{\beta }_1}$ for $p>\mathrm{}{p}_c.$ Monte Carlo simulations yield ${\beta }_1=\mathrm{0.81.}\mathrm{}$ A cluster approximation is developed for this model, qualitatively confirming the numerical results and predicting ${\beta }_1=1.\mathrm{}$ The singular behavior of the isolated particles density in the inactive phase is explained using a phenomenological approach.