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)similar or equal to 0.50(W similar to t(w)(beta)). At criticality the growth presents a crossover at a characteristic time t(c), from a correlated regime (with beta(w)not equal 0.50) to an uncorrelated one (beta(w)similar or equal to 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.