Ising Variables Research Articles

Discrete Hubbard-Stratonovich transformation for fermion lattice models

We discuss a new functional-integral formulation of interacting fermion systems on a lattice such as the Anderson or Hubbard models: the fermion-fermion interaction is eliminated by introducing auxiliary Ising variables. The resulting model for a $d$-dimensional quantum system is a ($d+1$)-dimensional Ising model with complicated interactions. The new transformation is particularly useful for performing numerical studies of these models using Monte Carlo techniques. We study its convergence properties and compare it with the usual Gaussian formulation for the case of the Hubbard model.

A study of order in deuterated ammonium chloride by neutron scattering

The diffuse neutron scattering intensity from a single crystal of ND4Cl in the room temperature beta phase is studied in detail in the (h,h,l plane as a function of temperature. An Ising model is set up which includes the interaction of the Ising variables with the ionic displacements. The temperature and reciprocal space dependences of the diffuse intensity are calculated using a mean field approximation and are fitted to the observed data, yielding Ising interaction energies. Two models of the ND4Cl structure are set up to calculate these interaction energies: the first assumes electrostatic interactions only and leads to a value for the Cl- ion polarizability of 2 AA3 which is too low. The second model is based on a 'shell' model for Cl-, incorporates short-range interactions, and accounts for the interaction energies assuming the known polarizability. Both models give a deuterium charge of greater than 0.3e which indicates shortcomings in the mean field approximation.