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The Ising square lattice in aL×M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers

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Zeitschrift für Physik B Condensed Matter

Abstract

Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthM≫L, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a “terrace” of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary “fields” is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the boundary). Extensive Monte Carlo calculations on this model performed on a multi-transputer system are presented and analyzed in terms of phenomenological finite size scaling concepts. The fact that two scaling variables occur (ζ/L,L/M, with ζ being the correlation length in the bulk) is demonstrated explicitly. In the absence of boundary fields, the system forM≫L orders nearT c in a domain state, with domain walls running across the terrace, while at some temperature belowT c a transition to a monodomain state occurs. This domain state slightly belowT c is suppressed, however, by rather weak boundary fields. These results are interpreted in terms of exact theoretical predictions.

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Author notes

  1. E. V. Albano (Alexander of Humboldt-Fellow)

    Present address: INIFTA, Universidad de La Plata, C.C. 16, Suc. 4, 1900, La Plata, Argentina

Authors and Affiliations

  1. Institut für Physik, Johannes Gutenberg-Universität Mainz, Postfach 3980, D-6500, Mainz, Federal Republic of Germany

    E. V. Albano (Alexander of Humboldt-Fellow), K. Binder, Dieter W. Heermann & W. Paul

  2. Fachbereich Physik, Universität Wuppertal, FRG

    Dieter W. Heermann

Authors
  1. E. V. Albano
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  2. K. Binder
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  3. Dieter W. Heermann
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  4. W. Paul
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Albano, E.V., Binder, K., Heermann, D.W. et al. The Ising square lattice in aL×M geometry: A model for the effect of surface steps on phase transitions in adsorbed monolayers. Z. Physik B - Condensed Matter 77, 445–460 (1989). https://doi.org/10.1007/BF01453796

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  • DOI: https://doi.org/10.1007/BF01453796

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