R. Rangel and L. E. Guerrero, Fractals 3, 533 (1995). Reprinted in: Fractal Geometry and Analysis, The Mandelbrot Festschrift, Curaçao 1995, edited by C. J. G. Evertsz, H.-O. Peitgen, and R. F. Voss (World Scientific, Singapore, 1996) pp. 129-135
Anomalous roughening in a random sine Gordon chain
The appearance of solitons in a random sine-Gordon system is related to the roughening exponent, z, defined as the scaling exponent of the length of the ensemble average of the standard deviation of the height of the spatiotemporal profile. We show that the coherence of the ordered state appears to have three different regimes with well-defined crossover lengths. After the activation of solitons, there is a very interesting crossover from non-Kardar-Parisi-Zhang behavior (z ~ 0.7) to KPZ behavior (z ~ 0.5); additionally, for sufficiently large scales, a crossover to a zero roughening exponent takes place. For the transient we calculate from flat initial conditions the common dynamic exponent (z/z ~ 0.9) for all these regimes. This last result reveals that the surface grows faster than is predicted by the KPZ model. We point out the connection of our results to the Sneppen universality class and discuss the crossover between the conditions of global dynamics and the conditions of local dynamics at different length scales in the stationary regime.