Bloch electron in a magnetic field and the Ising model
Igor V. Krasovsky
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Submission date: 02. Mar. 2000
published in: Physical review letters, 85 (2000) 23, p. 4920- 4923
DOI number (of the published article): 10.1103/PhysRevLett.85.4920
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The spectral determinant of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux 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.