The solid-on-solid surface width around the roughening transition

H.G. Evertz, M. Hasenbusch, M. Marcu, Klaus Pinn

Research output: Contribution to journalArticlepeer-review


We investigate the surface width W of solid-on-solid surfaces in the vicinity of the roughening temperature Tr. Above Tr, W2 is expected to diverge with the system size L like ln L. However, close to Tr 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 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).
Original languageEnglish
Pages (from-to)31-39
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
Publication statusPublished - 1993
Externally publishedYes


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