THE SOLID-ON-SOLID SURFACE WIDTH AROUND THE ROUGHENING TRANSITION

We investigate the surface width W of solid-on-solid surfaces in the vicinity of the roughening temperature T(r). Above T(r), W2 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 x L square lattice. In the simulation we took 8 less-than-or-equal-to L less-than-or-equal-to 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).