for other exponents due to the sensitivity to the uncertainty in the determination of the critical point.

It was proved in [@MN1; @MN2] that these exponents must satisfy the scaling relation $z= \beta/(\nu_\bot \theta)$, where $z$ is the dynamic exponent of the KPZ equation. The exact value for $z$ in $d=1$ is $3/2$, thereby $z = 0.33 / 0.215 = 1.5(1)$ in agreement with the prediction. In addition, also from [@MN1; @MN2], $\nu_\bot =1$, and from our direct measurements we get $(\beta_n/\nu_\bot)/ \beta_n = 0.33/0.32$, implying $\nu_\bot \approx 1$. In terms of $h$ and assuming $\nu_\bot=1$, $z=0.52/.355= 1.5(1)$ which, again, is compatible with $3/2$ within error bars.

The two alternative, but equivalent, mathematical descriptions of the MN2 class in terms of $h$ and $n=\exp(-h)$ can be related noting that the latter is essentially the density of sites at zero hight, $n(x,t)=\delta_{h(x,t),0}$ [@Haye3]. We have verified that $n$ and $\delta_{h(x,t),0}$ exhibit the same asymptotic scaling behavior.

![Model 1: steady-state values of the oder parameter, $\n =\langle
\exp h \rangle$, as function of the system size, $L$, for drifts (top to bottom) 1.57450, 1.57440, 1.57435, 1.57433, 1.57430, 1.57425, 1.57420. $\langle \cdot \rangle$ denotes both spatial and temporal averages, as well as averages 