The contact process in heterogeneous and weakly-disordered systems

The critical behavior of the contact process (CP) in heterogeneous periodic and weakly-disordered environments is investigated using the supercritical series expansion and Monte Carlo (MC) simulations. Phase-separation lines and critical exponents $\beta$ (from series expansion) and $\eta$ (from MC simulations) are calculated. A general analytical expression for the locus of critical points is suggested for the weak-disorder limit and confirmed by the series expansion analysis and the MC simulations. Our results for the critical exponents show that the CP in heterogeneous environments remains in the directed percolation (DP) universality class, while for environments with quenched disorder, the data are compatible with the scenario of continuously changing critical exponents.