Frustrated Magnetic Systems and the $Q$-Oscillator

We analyse the Spherical Model with frustration induced by an external gauge field. In indefinite dimensions, this model has been recently mapped onto a problem of q-deformed oscillators, $q$ 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 behaviour. The effect of frustration is only quantitative, with respect to the usual unfrustrated Spherical Model. A glassy low-temperature phase is anyway expected for the more complicated XY Model, whose study is in progress.