QUANTUM VERSION OF A SPHERICAL MODEL - CROSSOVER FROM QUANTUM TO CLASSICAL CRITICAL-BEHAVIOR

We investigate a quantum version of the spherical model which is obtai ned from the classical Berlin-Kac spherical model by a simple canonica l quantization scheme. We find a complete solution of the model for sh ort-range as well as for long-range interactions. At finite temperatur es the critical behavior is the same as in the classical spherical mod el whereas at zero temperature we find a quantum phase transition char acterized by new critical exponents. Based on a functional-integral re presentation of the partition function the free energy of the model is shown to be equivalent to that of the nonlinear a model in the limit of infinite order-parameter dimensionality.