in Eq. (\[mnminus\]) cannot be readsorbed by reparametrizing.

Finally, let us underline that in the regime where $b<0$ the wall becomes attractive (which might be necessary to describe some physical situations as, for instance, synchronization problems as said in the introduction) and a new term, say, $c \exp(-2h)$ (equivalently $c n^{2p+1}$) with $c>0$ has to be added to stabilize the equation.

Having presented the equations defining the model, in the forthcoming sections we study the associated physics by using i) mean field approaches, ii) field theory, and iii) numerical, Monte Carlo simulations combined with scaling arguments.

Mean-field approaches
=====================

Mean-field approaches to Eq. (\[BKPZ\]) can be implemented with several degrees of sophistication. A crude approximation consists of ignoring the noise and spatial variations. At this level one trivially gets that the order parameter $\langle h \rangle$ vanishes as $a \to 0$ with an exponent $\beta_h=0$. When applied to Eq.(\[mnminus\]), this approximation yields a shifted critical point at $a_c=-1$ and the usual result for the order parameter critical exponent, $\beta_n=1/p$. But, as experience with other systems with multiplicative-noise dictates, neglecting completely the noise is a too crude approximation, that eliminates most of the characteristic traits of MN physics.

Now the effect 