Solving the Frustrated Spherical Model with q-Polynomials

Details Solving the Frustrated Spherical Model with q-Polynomials Solving the Frustrated Spherical Model with q-Polynomials

1997-10-08

arxiv.org/abs/hep-th/9710071v1

J.Phys.A31:3141-3151,1998

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 14 pages, 2 eps figures

Scientific paper

10.1088/0305-4470/31/14/004

We analyse the Spherical Model with frustration induced by an external gauge field. In infinite dimensions, this has been recently mapped onto a problem of q-deformed oscillators, whose real parameter q measures the frustration. We find the analytic solution of this model by suitably representing the q-oscillator algebra with q-Hermite polynomials. We also present a related Matrix Model which possesses the same diagrammatic expansion in the planar approximation. Its interaction potential is oscillating at infinity with period log(q), and may lead to interesting metastability phenomena beyond the planar approximation. The Spherical Model is similarly q-periodic, but does not exhibit such phenomena: actually its low-temperature phase is not glassy and depends smoothly on q.

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