Abstract
The ferromagnetic two-dimensional XY model with a p-fold symmetry-breaking field Hp, subjected to an in-plane external field H applied at an angle omega (0<or= omega <or= pi /p) with respect to the p-fold axis, is analyzed exactly at zero temperature. A spin-flip-type transition occurs at a critical field Hc=p2Hp and at a critical angle omega 0= pi /p. At this critical point, the parallel differential susceptibility, chi /sub /// (where the probing field h/sub /// is parallel to H), jumps discontinuously to zero and the perpendicular differential susceptibility, chi perpendicular to (where the probing field hperpendicular to is perpendicular to H), diverges like (HC-H)-12/. A self-consistent harmonic approximation is applied for the low-temperature analysis and numerical results for the magnetisation, the parallel susceptibility and the perpendicular susceptibility are obtained. The singularities of the zero-temperature analysis are retained when random averages are taken numerically over the angle omega for the parallel susceptibility and magnetisation. Implications on the measurements of the magnetic properties of two-dimensional systems are discussed.
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