Schramm–Loewner evolution theory of the asymptotic behaviors of (2+1)-dimensional Das Sarma–Tamborenea model

Abstract

A mass of theoretical analysis and numerical calculation on (2+1)-dimensional Das Sarma–Tamborenea model have been carried out over the years. A problem about asymptotical behaviors that this model belongs to which universality classes is still interesting and controversial. The Schramm–Loewner evolution theory is an innovative point of view to describe the conformal invariance of contour lines of saturated rough surfaces. In this paper, we used SLE theory to analyze the conformal invariance of the (2+1)-dimensional DT model. A noise reduction technique was also utilized to get better scaling behavior. The results show that the contour lines of (2+1)-dimensional DT model satisfy the property of conformal invariance and belongs to κ=4 universality class. The relation df=1+κ∕8 is also satisfied for the fractal dimension and diffusion coefficient of the contour lines.