Magnets with random uniaxial anisotropy: Large- N effective potential and infrared properties

Abstract

We study the magnetic properties of systems with random uniaxial anisotropy using a large- N effective potential approach for d = 4, 3. It is found that the random interactions induce a strong infrared behavior that prevents the existence of a ferromagnetic phase and massless transverse modes. The transverse susceptibility is finite for all values of the temperature and at d = 4 it has an esential singularity in the couplings. We argue that this is indicative of a mechanism of dynamical mass generation due to the infrared instabilities of the theory. For both d = 4, 3 there is a spin-glass low-temperature phase and a paramagnetic high-temperature phase, the susceptibility having a cusp across the transition. We prove that these phases are stable and that the transverse and longitudinal susceptibilities are equal.