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

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

Physica A: Statistical Mechanics and its Applications, 1993, vol. 199, issue 1, 31-39

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).

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:199:y:1993:i:1:p:31-39

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

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