For the two-dimensional ferromagnetic Ising critical point, I show that the known values of the critical exponents imply the absence of logarithms of the reduced temperature in the leading contributions to any field derivative of the free energy at zero magnetic field. For the square-lattice Ising antiferromagnet in a weak magnetic field, I compute the critical line Tc(H)=Tc0(1-0.038 023 259H2) and the leading contribution to the susceptibility χ=0.014 718 006 6H2ln(1/ǁtǁ), where t is the reduced temperature.