Accession Number : AD0747736

Title :   Field Theory of the Two-Dimensional Ising Model: Equivalence to the Free Particle One-Dimensional Dirac Equation.

Descriptive Note : Technical rept.,

Corporate Author : MARYLAND UNIV COLLEGE PARK CENTER FOR THEORETICAL PHYSICS

Personal Author(s) : Ferrell,Richard A.

Report Date : MAY 1972

Pagination or Media Count : 28

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)

Descriptors :   (*PHASE STUDIES, MATHEMATICAL MODELS), FIELD THEORY, FERMIONS, MATRICES(MATHEMATICS)

Subject Categories : Physical Chemistry
      Solid State Physics

Distribution Statement : APPROVED FOR PUBLIC RELEASE