Geodesic
Frustrated Magnetic Systems and the $Q$-Oscillator
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 15, Tome 251 (1998), pp. 57-68

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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. 
@article{ZNSL_1998_251_a5,
     author = {A. Cappelli and F. Colomo},
     title = {Frustrated {Magnetic} {Systems} and the $Q${-Oscillator}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {57--68},
     publisher = {mathdoc},
     volume = {251},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_251_a5/}
}
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A. Cappelli; F. Colomo. Frustrated Magnetic Systems and the $Q$-Oscillator. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 15, Tome 251 (1998), pp. 57-68. http://geodesic.mathdoc.fr/item/ZNSL_1998_251_a5/