Scaling properties of self-expanding surfaces

Roughening of k-mer-growing interfaces in stationary regimes

We discuss the steady-state dynamics of interfaces with periodic boundary conditions arising from body-centered solid-on-solid growth models in 1+1 dimensions involving random aggregation of extended particles (dimers, trimers, ...,k-mers). Roughening exponents as well as width and maximal height distributions can be evaluated directly in stationary regimes by mapping the dynamics onto an asymmetric simple exclusion process with k-type of vacancies. Although for k≥2 the dynamics is partitioned into an exponentially large number of sectors of motion, the results obtained in some generic cases strongly suggest a universal scaling behavior closely following that of monomer interfaces.

Scaling and width distributions of parity-conserving interfaces

We present an alternative finite-size approach to a set of parity-conserving interfaces involving attachment, dissociation, and detachment of extended objects in 1+1 dimensions. With the aid of a nonlocal construct introduced by Barma and Dhar in related systems [Phys. Rev. Lett. 73, 2135 (1994)], we circumvent the subdiffusive dynamics and examine close-to-equilibrium aspects of these interfaces by assembling states of much smaller, numerically accessible scales. As a result, roughening exponents, height correlations, and width distributions exhibiting universal scaling functions are evaluated for interfaces virtually grown out of dimers and trimers on large-scale substrates. Dynamic exponents are also studied by finite-size scaling of the spectrum gaps of evolution operators.

Nonuniversal dynamics of dimer growing interfaces

A finite temperature version of body-centered solid-on-solid growth models involving attachment and detachment of dimers is discussed in 1+1 dimensions. The dynamic exponent of the growing interface is studied numerically via the spectrum gap of the underlying evolution operator. The finite size scaling of the latter is found to be affected by a standard surface tension term on which the growth rates depend. This nonuniversal aspect is also corroborated by the growth behavior observed in large scale simulations. By contrast, the roughening exponent remains robust over wide temperature ranges.

Roughness of two-dimensional surfaces with global constraints

We study dynamical scaling properties of the two-dimensional surface growth models with global constraints. These include the growth model from a partition function Z = sigma{(h(r)Pi(h = h)(min) (h(max)) 1/2 (1 + z (n(h))), multiparticle-correlated surface growth models and dissociative Q-mer growth models. The equilibrium surfaces of all the models except the dimer model show the same dynamical scaling behavior W2 (L,t) = (1/2piK(G)) ln [L g (t/L(z(W)))] with z(W) = 2.5 and K(G) = 0.916 , whereas the surface in the dimer model has a correction to the scaling. The growing (eroding) surfaces have two phases. The models with z > or = 0 show the normal Kardar-Parisi-Zhang scaling behavior. In contrast the models with -1 < or = z < 0 and multiparticle-correlated growth model manifest grooved surface structures with alpha = 1. The growing surfaces of Q -mer models form rather complex facets.