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It is shown that the eigenvalue problem for the hermitian Wilson-Diracoperator of for a uniform magnetic field in two dimensions can be reduced toone-dimensional problem described by a relativistic analog of the Harperequation. An explicit formula for the secular equations is given in term of aset of polynomials. The spectrum exhibits a fractal structure in the infinitevolume limit. An exact result concerning the index theorem for the overlapDirac operator is obtained.Comment: 8 pages, latex, 3 eps figures, minor correction

Spectrum of the Hermitian Wilson-Dirac operator for a uniform magnetic field in two dimensions