Competing field-induced transition in the two-dimensional xy model

The ferromagnetic two-dimensional XY model with a p-fold symmetry-breaking field H_p, subjected to an in-plane external field H applied at an angle ω (0 ≤ ω ≤ ππρp) with respect to the p-fold axis, is analysed exactly at zero temperature. A spin-fiip-type transition occurs at a critical field H_c = p²H_p and at a critical angle ω = π/p. At this critical point, the parallel differential susceptibility, x₁ (where the probing field h₁ is parallel to H), jumps discontinuously to zero and the perpendicular differential susceptibility, x (where the probing field h_is perpendicular to H), diverges like (H_c 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 to for the parallel susceptibility and magnetisation. Implications on the measurements of the magnetic properties of two-dimensional systems are discussed.