# 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):

# 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

# Subject Categories:

- Physical Chemistry
- Solid State Physics