Theory of a spherical-quantum-rotors model: Low-temperature regime and finite-size scaling

The quantum-rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a d-dimensional model in the spherical approximation confined to a general geometry of the form L(d-d')x infinity(d') x L-tau(z) (L-linear space size and L-tau-temporal size) and subjected to periodic boundary conditions. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phe nomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions 1<d<3 and 0 less than or equal to d less than or equal to d a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.