The Solid-on-Solid Surface Width Around the Roughening Transition
نویسندگان
چکیده
We investigate the surface widthW of solid-on-solid surfaces in the vicinity of the roughening temperature Tr. Above Tr, W 2 is expected to diverge with the system size L like lnL. However, close to Tr a clean lnL 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 Tr. 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×L square lattice. In the simulation we took 8 ≤ L ≤ 256. The improved formula fits the numerical results very well. From the analysis, we estimate the roughening temperature to be Tr = 0.755(3).
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