Abstract
We analyze the spherical model with frustration induced by an external gauge field. The case of the infinite-dimensional model has recently been reduced to a problem of q-deformed oscillators with q parametrizing the amount of frustration. We find a complete analytic solution of the model by using a convenient representation of the q-oscillator algebra, the q-Hermite polynomials. The low-temperature phase does not exhibit a glassy behavior. With respect to the usual unfrustrated spherical model, the effect of frustration is only quantitative. A glassy low-temperature phase is expected for the more complicated XY model whose study is in progress. Bibliography: 15 titles.
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