The isotropic N-vector model in random magnetic fields
Stevenson, Paul M.
Master of Science
We have investigated the dynamics of the isotropic N-vector model with long-range exchange couplings in random magnetic fields using a 1/N expansion. The leading order is exactly solved, showing the existence of a ferromagnetic phase separated from the disordered paramagnetic phase by a line. The critical behaviour of the system has been examined in the next-to-leading order of the 1/N expansion, showing that the critical exponents are by no means related to the ones of the pure system in d-2 dimensions. The ordered phase has been also investigated in the next-to-leading order, revealing a typical Goldstone behaviour of the non time-persistent part of the transverse fluctuations. For the longitudinal fluctuations, two different types of coexistence singularities emerge, one from the non time-persistent (as in the pure systems), vanishing with the temperature, and a more divergent one from the time-persistent part of the correlation.
Condensed matter physics