Lattice Magnetic Walks

Details Lattice Magnetic Walks Lattice Magnetic Walks

1993-10-13

arxiv.org/abs/cond-mat/9310024v1

Physics

Condensed Matter

31 pages, Plain TeX, 2 figures (available upon request), UR-CM-93-10-13

Scientific paper

10.1088/0305-4470/27/2/015

Sums of walks for charged particles (e.g. Hofstadter electrons) on a square lattice in the presence of a magnetic field are evaluated. Returning loops are systematically added to directed paths to obtain the unrestricted propagators. Expressions are obtained for special values of the magnetic flux-per-plaquette commensurate with the flux quantum. For commensurate and incommensurate values of the flux, the addition of small returning loops does not affect the general features found earlier for directed paths. Lattice Green's functions are also obtained for staggered flux configurations encountered in models of high-Tc superconductors.

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