Investigating the effect of quenched noise in continuous surface growth models

The Mullins–Herring equation is an important model in surface growth. This research aimed to explore quenched noise on this model using a new approach. The key point in this model is combination of the external force on the interface and quenched noise on one part with its strength adjusted with an external controllable parameter, g. It is shown that the dynamics of this model for some values of g have critical behaver. Also, our calculations show that, for g = 1 and 2 values there is no phase transition. The important feature of criticality is the existence of scaling exponents which in this study were computed numerically. As a result, for g = 3 the critical point was obtained (0.6504). At this point, the total roughness exponent and local roughness exponent were obtained (1.410 and 1.011), respectively. The inequality of these two values, that is the total and local roughness exponents, is one of the most important effects of quenched noise in growth models which indicates the variation in structure of the produced surface.