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

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  • Evertz, Hans Gerd
  • Hasenbusch, Martin
  • Marcu, Mihai
  • Pinn, Klaus

Abstract

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).

Suggested Citation

  • Evertz, Hans Gerd & Hasenbusch, Martin & Marcu, Mihai & Pinn, Klaus, 1993. "The solid-on-solid surface width around the roughening transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 199(1), pages 31-39.
    • Handle: RePEc:eee:phsmap:v:199:y:1993:i:1:p:31-39
    DOI: 10.1016/0378-4371(93)90094-K
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