Upper and Lower Bounds on the Partition Function of the Hofstadter Model

Details Upper and Lower Bounds on the Partition Function of the Hofstadter Model Upper and Lower Bounds on the Partition Function of the Hofstadter Model

1996-01-19

arxiv.org/abs/cond-mat/9601083v2

Mod.Phys.Lett. B10 (1996) 409-416

Physics

Condensed Matter

10 pages, plain latex, no figures. A section on bounds on the derivatives of the partition function and one reference added, t

Scientific paper

10.1142/S0217984996000468

Using unitary equivalence of magnetic translation operators, explicit upper and lower convex bounds on the partition function of the Hofstadter model are given for any rational ``flux" and any value of Bloch momenta. These bounds (i) generalize straightforwardly to the case of a general asymmetric hopping and to the case of hopping of the form $t_{jn}(S_j^n+S_j^{-n})$ with $n$ arbitrary integer larger than or equal $2$, and (ii) allow to derive bounds on the derivatives of the partition function.

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