1992/05/01 by Leon Balents, Balents, Leon, Mehran Kardar +1
Mathematics · Physics and Astronomy · #Quantum many-body systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9205002
33 pages including 12 figures
arxiv created 1992/05/01 · arxiv updated 2009/11/30
We consider a model of a reconstructed crystal surface, first considered by Villain and Vilfan (Europhys. Lett. 12, p. 523 (1990) and Surf. Sci. 257, p. 368 (1991)) for the gold (110) surface, in which roughening occurs via the formation of anisotropic steps traversing the entire length of the crystal. The model is studied by a mapping to a spin--1/2 Fermion system in 1+1 dimensions, which, in the absence of islands, is precisely the Hubbard model. We consider a general \pbyo reconstruction, in the presence of inter--step interactions and closed islands. Our analysis predicts the existence of a new type of rough phase, with incommensurate correlations in the reconstruction order parameter and unusual momentum space singularities at a characteristic ``Fermi momentum'' and its harmonics, analagous to the Luttinger liquid of one--dimensional Fermions. The general phase structure for p>1 is as follows: for p>2, there is a flat ordered (FO), a rough incommensurate (RI), and a flat incommensurate phase (FI). The FO--RI and FO--FI transitions are of the commensurate to incommensurate type, and the FI--RI transition is in the Kosterlitz--Thouless (KT) universality class. For p=2, the FI phase is replaced by a flat disordered phase (FD), and there may be a new rough disordered phase (RD). The FO--FD transition is now of Ising type, and the FD--RD and RI--RD transitions are in the KT universality class.