DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click

HERE to register or log in.

# 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

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#