CHAOS IN THE HERMITIAN ONE-MATRIX MODEL

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Abstract
The recursion coefficients Ri, which appear in the orthogonal polynomial method of solution for the Hermitian one-matrix model, are determined numerically for values of N up to a thousand. For some cases a chaotic behavior appears in some range, preventing a smooth flow from odd to even multicrititical models. This behavior is studied both for single-well and multiwell potentials. For multiwell potentials, the coefficients Ri generically tend toward more than one function in the N→∞ limit, and this structure is analyzed for small i using the Gaussian approximation.

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