In the paper of "The spectrum of difference operators and algebraic curves", by P. van Moerbeke and D. Mumford, Acta Mathematics, vol.143, 1979, (link: http://www.dam.brown.edu/people/mumford/alg_geom/papers/1979a--SpectrumDiffOps-NC.pdf) the following paper of Mumford is cited:
[26] Mumford, D. The Spectra of Laplace-like periodic partial difference operators and algebraic surfaces, to appear.
It seems I can't find this paper. Did it appear under a different name?