Llas Mateu, Gleiser Pablo M, López Juan M, Díaz-Guilera Albert
Departament de Física Fonamental, Universitat de Barcelona, Avenida Diagonal 647, E-08028 Barcelona, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Dec;68(6 Pt 2):066101. doi: 10.1103/PhysRevE.68.066101. Epub 2003 Dec 15.
We characterize the different morphological phases that occur in a simple one-dimensional model of propagation of innovations among economic agents [X. Guardiola et al., Phys. Rev E 66, 026121 (2002)]. We show that the model can be regarded as a nonequilibrium surface growth model. This allows us to demonstrate the presence of a continuous roughening transition between a flat (system size independent fluctuations) and a rough phase (system size dependent fluctuations). Finite-size scaling studies at the transition strongly suggest that the dynamic critical transition does not belong to directed percolation and, in fact, critical exponents do not seem to fit in any of the known universality classes of nonequilibrium phase transitions. Finally, we present an explanation for the occurrence of the roughening transition and argue that avalanche driven dynamics is responsible for the novel critical behavior.
我们刻画了经济主体间创新传播的简单一维模型中出现的不同形态阶段[X. 瓜迪奥拉等人，《物理评论E》66，026121(2002)]。我们表明该模型可被视为一个非平衡表面生长模型。这使我们能够证明在平坦（与系统大小无关的涨落）和粗糙阶段（与系统大小有关的涨落）之间存在连续的粗糙化转变。在转变点进行的有限尺寸标度研究强烈表明，动态临界转变不属于定向渗流，事实上，临界指数似乎并不符合任何已知的非平衡相变普适类。最后，我们对粗糙化转变的发生给出一种解释，并认为雪崩驱动动力学是这种新奇临界行为的原因。
