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MiS Preprint
20/2000
Bloch electron in a magnetic field and the Ising model
Igor V. Krasovsky
Abstract
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.
