Surface growth studies
In Ref.  we introduced a model for the growth of an interface by dimer adsorption and desorption. Dimers (composite particles consisting of two atoms) are adsorbed at sites of equal height at rate p and evaporate at rate 1-p. The key feature of our model is that evaporation is allowed only at the edges of terraces. In 1+1 dimensions the dynamic rules are:
One of the most interesting properties of this model is a roughening transition from a smooth to a rough phase at the critical threshold p=0.3167. The following figure illustrates typical interface morphologies for various values of p:
Restricted solid on solid (RSOS)
Unrestricted solid on solid (SOS) version
In the smooth phase, the interface selects spontaneously one height level as the bottom layer of the interface. The roughening transition is related to the so-called parity-conserving universality class (PC) which is represented most prominently by branching-annihilating random walks with two offspring A->3A, 2A->0. In such a process the particle density vanishes according to a power law with a certain critical exponent
n ~ (p-pc)0.92.
It can be shown that the density of exposed sites at the bottom
layer in our model vanishes with the same critical exponent, showing
that the roughening transition is closely related to the PC class. In
fact, the critical behavior at the first few layers may be explained
in terms of unidirectionally coupled PC processes:
In Ref.  we explored the phase
structure of several variants (SOS, RSOS,random sequential, parallel
update) of this model in the p=(0,1) region and show that all
variants display the same type of universal critical behavior at the
roughening transition. Besides the roughening transition there is a
faceting transition as well at
the symmetry point of the model (p=1/2). The scaling properties are
insensitive on whether we use parallel or random sequential updates.
If we start the system from random initial distribution of hights
the dynamical properties will be different as the consequence of
hard-core interactions. Moreover, a parity conserving polynuclear
growth model is proposed that exhibits the same critical behavior
at the roughening transition point as the dimer model.
This kind of mapping can be generalized to d-dimensions: the
surface deposition/removal corresponds to the migration of
directed d-mers of d-dimensional lattice gases. Hence, for
example the KPZ behavior can be studied by binary lattice gases
In three dimensions we have diffusing triangles with exclusions
as shown on the figure below.
For more details see Ref.  , Talk at Rathen ,  or talk of IINM-2011 (Bhubaneswar, India) arXiv:1109.2717.
Dec 18 2017