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:

1972-05-01

Pagination or Media Count:

28.0

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 12 power. Because k varies linearly with the temperature, differentiating twice gives Onsagers 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