2001/09/10 by D. E. Feldman · 66 citations
Chemistry · Economics, Econometrics and Finance · Physics and Astronomy · #Amorphous solid #Anisotropy #Chemistry #Complex Systems and Time Series Analysis #Condensed matter physics #Crystallography #Liquid crystal #Magnet #Materials science #Order (exchange) #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Range (aeronautics) #Spin glass #Superconductivity #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.soft
paper · pdf · doi:10.1142/s0217979201006641
published in International Journal of Modern Physics B 15(22), 2945-2976 (World Scientific) · 32 pages
openalex publication_date 2001/09/10 · arxiv created 2002/01/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider glass states of several disordered systems: vortices in impure superconductors, amorphous magnets, and nematic liquid crystals in random porous media. All these systems can be described by the random-field or random-anisotropy O(N) model. Even arbitrarily weak disorder destroys long range order in the O(N) model. We demonstrate that at weak disorder and low temperatures quasi-long range order emerges. In quasi-long-range-ordered phases the correlation length is infinite and correlation functions obey power dependencies on the distance. In pure systems quasi-long range order is possible only in the lower critical dimension and only in the case of Abelian symmetry. In the presence of disorder this type of ordering turns out to be more common. It exists in a range of dimensions and is not prohibited by non-Abelian symmetries.