• Preroughening in organic crystals
    R.F.P. Grimbergen, H. Meekes, P. Bennema, H.J.F. Knops, and M. den Nijs,
    Phys. Rev. B 58 , 5258-5265 (1998).

  • Preroughening transitions in a model for Si(001) and Ge(001) type crystal surfaces
    Jae-Dong Noh and Marcel den Nijs, Spring 1997, J.Phys. A 30 , 7375-7384 (1997).

  • Preroughening Induced Deconstruction in Si and Ge (001) Type Surfaces
    Marcel den Nijs, J.Phys. A 30, 397 (1997).

  • Roughening, Preroughening, and Reconstruction Transitions in Crystal Surfaces
    Marcel den Nijs, chapter 4 in The Chemical Physics of Solid Surfaces and Heterogeneous
    Catalysis, Vol.7 edited by D. King, Elsevier (Amsterdam, 1994).

  • Preroughening Transitions in Crystal Surfaces and Valence Bond States in Quantum Spin Chains
    Koos Rommelse and Marcel den Nijs, Phys.Rev. B 40, 4709 (1989).

  • Preroughening Transitions in Surfaces
    Koos Rommelse and Marcel den Nijs, Phys.Rev.Lett. 59, 2578-2581 (1987).

  • rough.gif

    Preroughening transitions take place in equilibrium crystal surfaces, typically near surface roughening transitions.

    They separate flat from so-called disordered flat (DOF) surface configurations. In DOF phases the steps on the surface are randomly placed, but follow long-range up-down order

    We discovered preroughening in 1987 in a numerical study of a solid-on-solid model with next nearest neighbour interactions.


    DOF phases are mathematically equivalant to so-called valence bond phases in one dimensional quantum spin chains (via the so-called transfer matrix formalism). The latter are quantum liquids with topological long range order with soliton like excitations. This equivalence elucidated the nature of long range order in the latter.


    In our early work, step-step interactions where required to stabilize DOF phases, but later we realized that directional anisotropy in step energies and more complex crystaline unit cells can have the same effect, e.g., in Si(001) and in Naphtalene.

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