  We present a solution of the non-linear renormalization group equations
leading to the dominant and subdominant singular behaviours of physical
quantities (free energy density, correlation length, internal energy, specific
heat, magnetization, susceptibility and magnetocaloric coefficient) at the
critical temperature in a non- vanishing magnetic field. The solutions i) lead
to exact cancellation of logarithmic corrections in universal amplitude ratios
and ii) prove recently proposed relations among logarithmic exponents.
