Rotated Heisenberg model

Fadi Sun, Jinwu Ye, Wu-Ming Liu

Arno Holz

The author establishes a relation between discrete excitation models at low temperature and the anisotropic rotator, XY and Heisenberg models at high temperature for dimensions D>or=2. The correlation functions of these models are shown to decay exponentially for short-range interactions. A qualitative discussion of the phase transitions is given.

S. Yu. Gubanov

Minoru Takahashi

Germán Sierra, Miguel Angel Martin-Delgado

We propose that the valence bonds forming the ground state of the 2D-AF Heisenberg model on a square lattice may rotate under the effect of the antiferromagnetic background. To test this idea we apply a real space renormalization group approach to construct a rotating-valence-bond ground state anstaz. Our results are analytic and valid for any value of the spin S of the AF-magnet, which allow us to perfom semiclassical expansions of the energy and the staggered magnetization.

Dennis C. Rapaport, David Paul Landau

We have performed large-scale molecular dynamics simulations of a dynamical variant of the classical Heisenberg model in which the spins are replaced by interacting "linear molecules," each of which has two rotational degrees of freedom. The Hamiltonian consists of rotational kinetic-energy terms as well as nearest-neighbor Heisenberg-like interactions $\ensuremath{-}J{\mathrm{s}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{s}}_{j}$, where ${\mathrm{s}}_{i}$ is a unit vector specifying the orientation of the molecule at lattice site $i$. Systems of size up to ${64}^{3}$ spins on the simple cubic lattice have been studied, and thermostatting is used to maintain strictly constant temperature. We determined the dynamic structure function from the time- and space-displaced correlation functions, and found good agreement with the predictions of the dynamic scaling theory with a dynamic critical exponent of $z=1.5$. Results are compared and contrasted with data from spin-dynamics calculations on classical Heisenberg ferromagnets and antiferromagnets.