Bloch electron in a magnetic field and the Ising model

Abstract

The spectral determinant det(H-εI) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux Φ=2πP/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.

4 pages, 1 figure, REVTEX

References in corpus (1)

• On the singular spectrum of the Almost Mathieu operator. Arithmetics and Cantor spectra of integrable models

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