Heisenberg models and a particular isotropic model

Heisenberg models and a particular isotropic model.

The Heisenberg model, a quantum mechanical analogue of the Ising model, has a large ground state degeneracy, due to the symmetry generated by the total spin. This symmetry is also responsible for degeneracies in the rest of the spectrum. We discuss the global structure of the spectrum of Heisenberg models with arbitrary couplings, using group theoretical methods. The Hilbert space breaks up in ...

A Criterion for Ferromagnetism in the Isotropic Quantum Heisenberg Model

A criterion for ferromagnetism is presented suggesting a line of proof to rigorously establish the phase transition. Spectral information will be required in certain invariant subspaces of the Hamiltonian, hopefully the relatively crude estimates needed will be not too difficult to establish.

Discrete skew selfadjoint canonical systems and the isotropic Heisenberg magnet model

A discrete analog of a skew selfadjoint canonical (Zakharov-Shabat or AKNS) system with a pseudo-exponential potential is introduced. For the corresponding Weyl function the direct and inverse problem are solved explicitly in terms of three parameter matrices. As an application explicit solutions are obtained for the discrete integrable nonlinear equation corresponding to the isotropic Heisenbe...

A fiber-reinforced Transversely Isotropic Constitutive Model for Liver Tissue

Biomechanical properties of soft tissue, such as liver, are important in modeling computer aided surgical procedures. Experimental evidences show that liver tissue is transversely isotropic. In this article, considering the liver tissue as an incompressible fiber-reinforced composite with one family of fibers, an exponential strain energy function (SEF) is proposed. The proposed SEF is based on...

A Necessary Condition for Weyl-Heisenberg Frames