The Schultz-Mattis-Lieb fermion formulation of the two-dimensional Ising model is simplified by means of long-wavelength approximations which become exact in the critical region. The resulting continuum theory has a Hamiltonian density which is shown to be identical, to within a perfect derivative, to that of free, spinless particles satisfying the one-dimensional Dirac equation. Filling the negative-energy single-particle states of momentumq and mass gives an integral over the single-particle energies -(2+k2)1/2. Because varies linearly with the temperature, differentiating twice gives Onsager's logarithmic singularity in the specific heat.