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.

Phase ordering dynamics of reconstituting particles.

We consider the large-time dynamics of one-dimensional processes involving adsorption and desorption of extended hard-core particles (dimers, trimers, ..., k-mers), while interacting through their constituent monomers. Desorption can occur whether or not these latter adsorbed together, which leads to reconstitution of k-mers and the appearance of sectors of motion with nonlocal conservation laws for k≥3. Dynamic exponents of the sector including the empty chain are evaluated by finite-size scaling analyses of the relaxation times embodied in the spectral gaps of evolution operators. For attractive interactions it is found that in the low-temperature limit such time scales converge to those of the Glauber dynamics, thus suggesting a diffusive universality class for k≥2. This is also tested by simulated quenches down to T=0, where a common scaling function emerges. By contrast, under repulsive interactions the low-temperature dynamics is characterized by metastable states which decay subdiffusively to a highly degenerate and partially jammed phase.

Metastable and scaling regimes of one-dimensional Kawasaki dynamics.

We investigate the large-time scaling regimes arising from a variety of metastable structures in a chain of Ising spins with both first- and second-neighbor couplings while subject to Kawasaki dynamics. Depending on the ratio and sign of these former, different dynamic exponents are suggested by finite-size scaling analyses of relaxation times. At low but nonzero temperatures these are calculated via exact diagonalizations of the evolution operator in finite chains under several activation barriers. In the absence of metastability the dynamics is always diffusive.

Low-temperature Glauber dynamics under weak competing interactions.

We consider the low but nonzero-temperature regimes of the Glauber dynamics in a chain of Ising spins with first- and second-neighbor interactions J1,J2. For 0<-J2/|J1|<1 it is known that at T=0 the dynamics is both metastable and noncoarsening, while being always ergodic and coarsening in the limit of T→0+. Based on finite-size scaling analyses of relaxation times, here we argue that in that latter situation the asymptotic kinetics of small or weakly frustrated -J2/|J1| ratios is characterized by an almost ballistic dynamic exponent z≃1.03(2) and arbitrarily slow velocities of growth. By contrast, for noncompeting interactions the coarsening length scales are estimated to be almost diffusive.

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.

Simulations of driven and reconstituting lattice gases.

We discuss stationary aspects of a set of driven lattice gases in which hard-core particles with spatial extent, covering more than one lattice site, diffuse and reconstruct in one dimension under nearest-neighbor interactions. As in the uncoupled case [M. Barma et al., J. Phys.: Condens. Matter 19, 065112 (2007)], the dynamics of the phase space breaks up into an exponentially large number of mutually disconnected sectors labeled by a nonlocal construct, the irreducible string. Depending on whether the particle couplings are taken attractive or repulsive, simulations in most of the studied sectors show that both steady state currents and pair correlations behave quite differently at low temperature regimes. For repulsive interactions an order-by-disorder transition is suggested.

Revisiting Kawasaki dynamics in one dimension.

Critical exponents of the Kawasaki dynamics in the Ising chain are re-examined numerically through the spectrum gap of evolution operators constructed both in spin and domain-wall representations. At low-temperature regimes the latter provides a rapid finite-size convergence to these exponents, which tend to z ≃ 3.11 for instant quenches under ferromagnetic couplings, while approaching to z ≃ 2 in the antiferro case. The spin representation complements the evaluation of dynamic exponents at higher temperature scales, where the kinetics still remains slow.

Nonuniversal nonequilibrium critical dynamics with disorder.

We investigate finite-size scaling aspects of disorder reaction-diffusion processes in one dimension utilizing both numerical and analytical approaches. The former averages the spectrum gap of the associated evolution operators by doubling their degrees of freedom, while the latter uses various techniques to map the equations of motion to a first-passage time process. Both approaches are consistent with nonuniversal dynamic exponents and with stretched exponential scaling forms for particular disorder realizations.

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.

Quantum approach to nucleation times of kinetic Ising ferromagnets.

Low temperature dynamics of Ising ferromagnets under finite magnetic fields are studied in terms of quantum spin representations of stochastic evolution operators. These are constructed for the Glauber dynamic as well as for its modification, introduced by Park [Phys. Rev. Lett. 92, 015701 (2004)]. In both cases the relaxation time after a field quench is evaluated both numerically and analytically using the spectrum gap of the corresponding operators. The numerical work employs standard recursive techniques following a symmetrization of the evolution operator accomplished by a nonunitary spin rotation. The analytical approach uses low temperature limits to identify dominant terms in the eigenvalue problem. It is argued that the relaxation times already provide a measure of actual nucleation lifetimes under finite fields. The approach is applied to square, triangular and honeycomb lattices.

Equilibrium of anchored interfaces with quenched disordered growth.

The roughening behavior of a one-dimensional interface fluctuating under quenched disorder growth is examined while keeping an anchored boundary. The latter introduces detailed balance conditions which allows for a simple but thorough analysis of equilibrium aspects at both macroscopic and microscopic scales. It is found that the interface roughens linearly with the substrate size only in the vicinity of special disorder realizations. Otherwise, it remains stiff and tilted.

Interfaces with a single growth inhomogeneity and anchored boundaries.

The dynamics of a one-dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an equilibrium stationary regime which allows for an exact calculation of roughening exponents. The stochastic evolution is related to a spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of late stages. For vanishing gaps the interface can exhibit a slow morphological transition followed by a change of scaling regimes which are studied numerically. Instead, a faceting dynamics arises for gapful situations.