Bloch electron in a magnetic field and the Ising model

Details Bloch electron in a magnetic field and the Ising model Bloch electron in a magnetic field and the Ising model

2000-04-03

arxiv.org/abs/cond-mat/0004018v1

Phys.Rev.Lett.85:4920-4923,2000

Physics

Condensed Matter

4 pages, 1 figure, REVTEX

Scientific paper

10.1103/PhysRevLett.85.4920

The spectral determinant det(H-\epsilon I) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux \Phi=2\pi P/Q through an elementary cell, where P and Q are coprime integers. The band edges of H correspond to the critical temperature of the Ising model; the spectral determinant at these (and other points defined in a certain similar way) is independent of P. A connection of the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is indicated.

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