Influence of diffusion on models for nonequilibrium wetting

It is shown that the critical properties of a recently studied model for nonequilibrium wetting are robust if one extends the dynamic rules by single-particle diffusion on terraces of the wetting layer. Examining the behavior at the critical point and along the phase transition line, we identify a special point in the phase diagram where detailed balance of the dynamical processes is partially broken.

Figure 1

Illustration of the dynamical rules. The transitions are (a) desorption at an edge, (b) desorption of a single atom, and (c) desorption out of the middle of a plateau. Panel (d) displays three different situations where an atom can be deposited. Furthermore the additional diffusive process considered in the present work is illustrated in (e).

Figure 2

Phase diagram of the model for nonequilibrium wetting introduced in Ref. 1 in one dimension. A line of continuous phase transitions separates the pinned and the moving phase. For $p=1$ the dynamical processes obey detailed balance (see text). Introducing diffusion shifts the phase transition line slightly but the overall structure of the phase diagram remains the same.

Figure 3

Breaking of detailed balance for $p\ne 1$. The figure shows four possible configurations of the interface together with the corresponding transition rates. If $P_A$ denoted the probability to find the interface in configuration $A$, detailed balance applied along the upper sequence of transitions would imply $P_C=q^2{P}_A$ while the lower sequence of transitions would give $P_C=(q^2∕p)P_A$. Therefore, this counterexample demonstrates that detailed balance is broken for $p\ne 1$.

Figure 4

Breaking of detailed balance by single-particle diffusion. A particle diffuses to the edge of an island where it sticks irreversibly. This process cannot be reversed so that detailed balance is broken.

Figure 5

(Color online) This graph shows that the width scales according to the Edwards-Wilkinson universality class as $w\sim t^{1∕4}$.

Figure 6

A possible configuration for a diffusive transition from site number $3$ to site number $4$. The arrows indicate those sites where atoms could adsorb or desorb, respectively. Obviously, the diffusive move shown here increases the number of sites susceptible to deposition by 1.

Figure 7

The mirror-symmetric configuration of the configuration shown in Fig. 6 obtained by reflections $h\to -h$ and $x\to -x$. Here a diffusive move increases the number of sites susceptible to desorption by 1, compensating the contribution of the configuration shown in Fig. 6.

Figure 8

(Color online) Data collapse for $p=0.3$ for different times.