  We investigate an explicite formula for ground state energy of the
anisotropic XY chain in transverse magnetic field. In particular, we examine
the smoothness properties of the expression, given in terms of elliptic
integrals. We confirm known 2d-Ising type behaviour in the neighbourhood of
certain lines of phase diagram and give more detailed information there,
calculating a few next-to-leading exponents as well as corresponding
amplitudes. We also explicitly demonstrate that the ground-state energy is
infinitely differentiable on the boundary between ferromagnetic and oscillatory
phases.
