1982/06/01 by P Bak, Per Bak · 14 citations
Physics and Astronomy · Chemistry · #Quantum chaos and dynamical systems #Molecular spectroscopy and chirality #Spectroscopy and Quantum Chemical Studies
paper · doi:10.1088/0034-4885/45/6/001
Modulated structures with periods which are incommensurable (or high-order com-mensurable) with the basic lattice are quite common in condensed-matter physics. The structure may be another lattice, a periodic lattice distortion, a helical or sinusoidal magnetic structure, or a charge density wave in one, two or three dimensions. This review surveys recent theories on the transition between commensurate (C) and incommensurate (I) phases, and on the properties of the ‘incommensurate ’ phase. The predictions of theories will be compared with experiments. The CI transition is usually described in terms of wall, or soliton, formation. The nature of the transition and the structure of the I phase are quite different in two and three dimensions. In three dimensions the I phase seems to consist of an infinity of high-order locked C phases, which may or may not be separated by an infinity of truly incommensurate phases. This behaviour is known as the ‘devil’s staircase’. In two dimensions the incommensurate phase (at T # 0) is a ‘floating ’ phase without complete long-range order, and it does not ‘lock-in ’ at high-order commensurate phases. Phase diagrams are determined by the stability of two types of ‘topological ’ defects: walls, which destabilise the C phase with respect to I phases, and dislocations or vortices which generate paramagnetic or fluid phases. A consequence of this competition is that for sufficiently low order of commensurability the C and I phases are separated by a fluid phase. The properties of modulated systems can be studied by iterating certain area-preserving two-dimensional maps. Very recent studies indicate that, in addition to C and I phases, there are chaotic structures which are at least metastable. The chaotic regimes separate C and I phases and may be described as randomly pinned solitons. The relevance of the chaotic regimes to adsorbed monolayers, pinning of charge density waves, Peierls transitions and spin glasses is briefly discussed. This review was received in July 1981.