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Field Theory of the Two-Dimensional Ising Model: Equivalence to the Free Particle One-Dimensional Dirac Equation.
MARYLAND UNIV COLLEGE PARK CENTER FOR THEORETICAL PHYSICS
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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 momentum q and mass k gives an integral over the single-particle energies -q squared k squared to the 12 power. Because k varies linearly with the temperature, differentiating twice gives Onsagers logarithmic singularity in the specific heat. Author
APPROVED FOR PUBLIC RELEASE