Abstract
We introduce a novel notion, order indices of reduced density matrices, characterizing different types of order, long-range as well as mid-range, occurring in statistical systems. The order indices define the behaviour of the largest eigenvalues of density matrices in the thermodynamic limit. These indices are especially useful for describing mid-range order, where they are directly connected with the large-distance asymptotic forms of off-diagonal density matrices. Several examples illustrate the idea.
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