Field Theory of the Two-Dimensional Ising Model: Equivalence to the Free Particle One-Dimensional Dirac Equation.
Abstract
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 1/2 power. Because k varies linearly with the temperature, differentiating twice gives Onsager's logarithmic singularity in the specific heat. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1972
- Accession Number
- AD0747736
Entities
People
- Richard A. Ferrell
Organizations
- University of Maryland