Order-parameter critical exponent of absorbing phase transitions in one-dimensional systems with two symmetric absorbing states

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent $\beta$ of absorbing phase transitions in systems with two symmetric absorbing states. The value of $\beta$ was conjectured to be $\frac{13}{14}\approx 0.93$ and Monte Carlo simulation studies in the literature have repeatedly reproduced values consistent with the conjecture. In this paper, we systematically estimate $\beta$ by analyzing the effective exponent after finding how strong corrections to scaling are. We show that the widely accepted numerical value of $\beta$ is not correct. Rather, we obtain $\beta = 1.020(5)$ from different models with two symmetric absorbing states.