Breakdown of universality in multi-cut matrix models

Bonnet, GORCID logo; David, F; Eynard, B and (2000) Breakdown of universality in multi-cut matrix models. Journal of Physics A: Mathematical and General, 33 (38). pp. 6739-6768. ISSN 0305-4470 DOI: 10.1088/0305-4470/33/38/307
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We solve the puzzle of the disagreement between orthogonal polynomials methods and mean-field calculations for random N×N matrices with a disconnected eigenvalue support. We show that the difference does not stem from a Bbb Z2 symmetry breaking, but from the discreteness of the number of eigenvalues. This leads to additional terms (quasiperiodic in N) which must be added to the naive mean-field expressions. Our result invalidates the existence of a smooth topological large-N expansion and some postulated universality properties of correlators. We derive the large-N expansion of the free energy for the general two-cut case. From it we rederive by a direct and easy mean-field-like method the two-point correlators and the asymptotic orthogonal polynomials. We extend our results to any number of cuts and to non-real potentials.


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This is an author accepted manuscript version of an article accepted for publication, and following peer review. Please be aware that minor differences may exist between this version and the final version if you wish to cite from it.
Available under Creative Commons: Attribution-NonCommercial-No Derivative Works 3.0

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