Technical Ferromagnetism

Reproduction and ferromagnetism

I present a stochastic population model that combines cooperative interactions of the type often used in physics with the process of reproduction and death familiar to biology, and I refer to reasons why such interlocking may be of interest to both fields. Physics and biology have developed good frameworks to model the process of stochastic change in systems which experience the action of coope...

A Theory of Ferromagnetism.

Ferromagnetism in Hubbard models.

We present the first rigorous examples of non-singular Hubbard models which exhibit ferromagnetism at zero temperature. The models are defined in arbitrary dimensions, and are characterized by finite-ranged hoppings, dispersive bands, and finite on-site Coulomb interaction U . The picture, which goes back to Heisenberg, that sufficiently large Coulomb interaction can revert Pauli paramagnetism ...

On two-dimensional ferromagnetism

We study the existence of minimizers for 2-dimensional ferromagnetism with various assumptions on different terms of the total energy. Our general philosophy for finding the minimizing magnetizations is to reduce this problem to a minimization problem for a new energy over a divergence-free field. Such a general philosophy works for all dimensions. However, in the twodimensional case, since the...

Pseudospin Quantum Hall Ferromagnetism

Symmetry breaking ground states occur in quantum Hall effect (QHE) systems when two or more Landau levels become degenerate near the Fermi level. Isotropic, easy-axis or easy plane quantum Hall ferromagnets (QHF) can form depending on the pseudospins of the involved Landau levels consisting of real spin, orbit radius quantum number, subband index or growth direction. Theories based on Hartree-F...