 Matrix order indices in statistical mechanicsV.I. Yukalov Physica A: Statistical Mechanics and its Applications, 2002, vol. 310, issue 3, 413-434 Abstract: A new notion of matrix order indices which relates the matrix norm and its trace is introduced. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well as nonequilibrium, for which the indices present a quantitative measure of the level of ordering. They characterize not only the long-range order, but also mid-range order. In the latter case, when order parameters do not exist, the matrix indices are well defined, providing an explicit classification of various mid-range orders. The matrix order indices are suitable for describing phase transitions with both off-diagonal and diagonal orders. Contrary to order parameters whose correct definition requires the thermodynamic limit, the matrix indices do not necessarily need the latter. Because of this, such indices can distinguish between different phases of finite systems, thus, allowing for the classification of crossover phase transitions. Keywords: Statistical systems; Phase transitions; Classification of orders (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:310:y:2002:i:3:p:413-434 DOI: 10.1016/S0378-4371(02)00783-5 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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