Quantum rotors in the presence of a random field

Abstract

We have studied the $M$-component quantum rotor Hamiltonian in the presence of a static random field (uncorrelated and Gaussian distributed) on each site of the lattice. This model is essentially an $M$-component generalization of the transverse Ising model in a random longitudinal field. We find that even the zero-temperature transition in the model from a ferromagnetic to the paramagnetic phase, is dominated by the random-field fixed point, which essentially determines the finite-temperature transition in the above model and the transition in the classical $M$-vector model in the presence of a random field. With the assumption that the transition is of continuous nature, we employ a standard renormalization-group method to study the effective classical action of the model and extract the exponents associated with the transition. We do also extend these renormalization-group calculations to the spherical $(\stackrel{\ensuremath{\rightarrow}}{M}\ensuremath{\infty})$ limit. Finally, we develop a scaling argument that describes the zero-temperature transition and clearly indicates the occurrence of the dynamical exponents in the different scaling relations. We also qualitatively discuss the dynamic scaling scenario in the quantum model.