The Solid-on-Solid Surface Width Around the Roughening Transition

H. G. Evertz; M. Hasenbusch; M. Marcu; K. Pinn

doi:10.1016/0378-4371(93)90094-K

paper

The Solid-on-Solid Surface Width Around the Roughening Transition

arXiv:cond-mat/9305029 · doi:10.1016/0378-4371(93)90094-K

Abstract

We investigate the surface width $W$ of solid-on-solid surfaces in the vicinity of the roughening temperature $T_{r}$ . Above $T_{r}$ , $W^{2}$ is expected to diverge with the system size $L$ like $ln L$ . However, close to $T_{r}$ a clean $ln L$ behavior can only be seen on extremely large lattices. Starting from the Kosterlitz-Thouless renormalization group, we derive an improved formula that describes the small $L$ behavior on both sides of $T_{r}$ . For the Discrete Gaussian model, we used the valleys-to-mountains-reflections cluster algorithm in order to simulate the fluctuating solid-on-solid surface. The base plane above which the surface is defined is an $L \times L$ square lattice. In the simulation we took $8 \leq L \leq 256$ . The improved formula fits the numerical results very well. {}From the analysis, we estimate the roughening temperature to be $T_{r} = 0.755 (3)$ .

9 pages, LaTeX (no figures), FSU-SCRI-93-67, CERN-TH.6893/93