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We consider the adjacency matrix associated with a graph that describestransitions between $2^{N}$ states of the discrete Preisach memory model. Thismatrix can also be associated with the last-in-first-out inventory managementrule. We present an explicit solution for the spectrum by showing that thecharacteristic polynomial is the product of Chebyshev polynomials. Theeigenvalue distribution (density of states) is explicitly calculated and isshown to approach a scaled Devil's staircase. The eigenvectors of the adjacencymatrix are also expressed analytically.

The Devil is in the Details: Spectrum and Eigenvalue Distribution of the Discrete Preisach Memory Model