One-dimensional contact process with both temporal and spatial disorder

We investigate the non-equilibrium phase transition in the contact process under the influence of both temporal and spatial disorder using large-scale Monte-Carlo simulations. Spatial disorder alone is known to lead to an exotic infinite-randomness critical point [1]. More recently, it was shown that temporal disorders also produces unconventional critical behavior dubbed infinite-noise critical behavior [2]. We perform a series of simulations adding weak temporal disorder to a spatially disordered space and vice versa. We find that the critical behavior remains unchanged by these perturbation, in agreement with the generalized Harris criteria [3]. We then focus on the case where both temporal and spatial disorder are strong.

[1] J. Hooyberghs et. al, Phys. Rev. Lett. 90, 100601 (2003). T. Vojta, M. Dickison, Phys. Rev. E 72, 036126 (2005).
[2] T. Vojta, J. Hoyos, Europhys. Lett. 112, 30002 (2015).
[3] T. Vojta, R. Dickman, Phys. Rev. E 93, 032143 (2016).