Quantum Lifshitz point: ε expansion and the spherical limit

Abstract

The quantum rotors are considered with regular frustration in the exchange couplings. In the zero-temperature phase diagram of the model the quantum disordered phase meets the ferromagnetic and helicoidal phase at the quantum Lifshitz point. Scaling behavior near the quantum Lifshitz point in D dimensions is consistent with the behavior near the classical Lifshitz point in D+z dimensions. The interesting feature is that z=1 for the anisotropic Lifshitz point and z=2 for the isotropic case. It is shown that the Lifshitz point exists for the anisotropy parameter m?6 and the helical ordering is obtained for m<D. The exponents associated with the quantum Lifshitz point, scaling relations, and the quantum-classical crossover exponent are also obtained in the spherical limit.