Two-dimensional XY and clock models studied via the dynamics generated by rough surfaces.

The p-state clock model is studied, for general values of p , from simulations using a heat-bath single spin flipping Monte Carlo method, and a mapping of the corresponding spinlike configurations to a solid-on-solid growth model. The growth exponents are calculated. From the dynamics generated by this far from equilibrium kinetic roughening of the surface one is able to characterize the corresponding equilibrium magnetic properties of the original model, such as the high temperature Berezinskii-Koserlitz-Thouless (BKT) transitions, the low-temperature long-range ordered phase transitions, as well as the conventional second-order phase transitions. The present method suggests that for p>or=5 the high-temperature phase transition is indeed a BKT one, whose value is the same as that for p-->infinity ( XY model), while the low-temperature phase transition has a first-order character.

Dynamics of rough surfaces generated by two-dimensional lattice spin models.

We present an analysis of mapped surfaces obtained from configurations of two classical statistical-mechanical spin models in the square lattice: the q -state Potts model and the spin-1 Blume-Capel model. We carry out a study of the phase transitions in these models using the Monte Carlo method and a mapping of the spin configurations to a solid-on-solid growth model. The first- and second-order phase transitions and the tricritical point happen to be relevant in the kinetic roughening of the surface growth process. At the low and high temperature phases the roughness W grows indefinitely with the time, with growth exponent beta(w) approximately 0.50(W approximately tbeta(w)) . At criticality the growth presents a crossover at a characteristic time tc, from a correlated regime (with beta(w) ++ 0.50 ) to an uncorrelated one (beta(w) approximately equal 0.50) . We also calculate the Hurst exponent H of the corresponding surfaces. At criticality, beta(w) and H have values characteristic of correlated growth, distinguishing second- from first-order phase transitions. It has also been shown that the Family-Vicsek relation for the growth exponents also holds for the noise-reduced roughness with an anomalous scaling.

Morphological transition between diffusion-limited and ballistic aggregation growth patterns.

In this work, the transition between diffusion-limited (DLA) and ballistic aggregation (BA) models was reconsidered using a model in which biased random walks simulate the particle trajectories. The bias is controlled by a parameter lambda, which assumes the value lambda=0 (1) for the ballistic (diffusion-limited) aggregation model. Patterns growing from a single seed were considered. In order to simulate large clusters, an efficient algorithm was developed. For lambda (not equal to) 0 , the patterns are fractal on small length scales, but homogeneous on large ones. We evaluated the mean density of particles (-)rho in the region defined by a circle of radius r centered at the initial seed. As a function of r, (-)rho reaches the asymptotic value rho(0)(lambda) following a power law (-)rho = rho(0) +Ar(-gamma) with a universal exponent gamma=0.46 (2) , independent of lambda . The asymptotic value has the behavior rho(0) approximately |1-lambda|(beta) , where beta=0.26 (1) . The characteristic crossover length that determines the transition from DLA- to BA-like scaling regimes is given by xi approximately |1-lambda|(-nu) , where nu=0.61 (1) , while the cluster mass at the crossover follows a power law M(xi) approximately |1-lambda(-alpha) , where alpha=0.97 (2) . We deduce the scaling relations beta=nugamma and beta=2nu-alpha between these exponents.