Exit probability in inflow dynamics: nonuniversality induced by range, asymmetry, and fluctuation.

Probing deeper into the existing issues regarding the exit probability (EP) in one-dimensional dynamical models, we consider several models where the states are represented by Ising spins and the information flows inwards. At zero temperature, these systems evolve to either of two absorbing states. The EP, E(x), which is the probability that the system ends up with all up spins starting with x fraction of up spins, is found to have the general form E(x)=xα/xα+(1-x)α. The EP exponent α strongly depends on r, the range of interaction, the symmetry of the model, and the induced fluctuation. Even in a nearest-neighbor model, a nonlinear form of the EP can be obtained by controlling the fluctuations, and for the same range, different models give different results for α. Nonuniversal behavior of the EP is thus clearly established and the results are compared to those of existing studies in models with outflow dynamics to distinguish the two dynamical scenarios.