Brito A Faissal, Redinz José Arnaldo, Plascak J A
Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, C. P. 702-30123-970, Belo Horizonte, MG, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 2):046106. doi: 10.1103/PhysRevE.75.046106. Epub 2007 Apr 9.
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.
q 态 Potts 模型和自旋 - 1 Blume - Capel 模型。我们使用蒙特卡罗方法以及将自旋构型映射到固 - 固生长模型，对这些模型中的相变进行了研究。一阶和二阶相变以及三临界点恰好与表面生长过程的动力学粗糙化相关。在低温和高温相中，粗糙度 W 随时间无限增长，增长指数β(w)约为 0.50（W 约为 tβ(w)）。在临界状态下，生长在特征时间 tc 处呈现出从相关区域（β(w) ++ 0.50）到不相关区域（β(w) 约等于 0.50）的转变。我们还计算了相应表面的赫斯特指数 H。在临界状态下，β(w)和 H 具有相关生长的特征值，可区分二阶相变和一阶相变。研究还表明，生长指数的 Family - Vicsek 关系对于具有反常标度的降噪粗糙度也成立。
