Green's-function theory of the Heisenberg ferromagnet in a magnetic field

We present a second-order Green's-function theory of the one- and two-dimensional S=1/2 ferromagnet in a magnetic field based on a decoupling of three-spin operator products, where vertex parameters are introduced and determined by exact relations. The transverse and longitudinal spin correlation functions and thermodynamic properties (magnetization, isothermal magnetic susceptibility, specific heat) are calculated self-consistently at arbitrary temperatures and fields. In addition, exact diagonalizations on finite lattices and, in the one-dimensional case, exact calculations by the Bethe-ansatz method for the quantum transfer matrix are performed. A good agreement of the Green's-function theory with the exact data, with recent quantum Monte Carlo results, and with the spin polarization of a $\nu=1$ quantum Hall ferromagnet is obtained. The field dependences of the position and height of the maximum in the temperature dependence of the susceptibility are found to fit well to power laws, which are critically analyzed in relation to the recently discussed behavior in Landau's theory. As revealed by the spin correlation functions and the specific heat at low fields, our theory provides an improved description of magnetic short-range order as compared with the random phase approximation. In one dimension and at very low fields, two maxima in the temperature dependence of the specific heat are found. The Bethe-ansatz data for the field dependences of the position and height of the low-temperature maximum are described by power laws. At higher fields in one and two dimensions, the temperature of the specific heat maximum linearly increases with the field.Comment: 9 pages, 9 figure

Absence of long-range order in a spin-half Heisenberg antiferromagnet on the stacked kagome lattice

We study the ground state of a spin-half Heisenberg antiferromagnet on the stacked kagome lattice by using a spin-rotation-invariant Green's-function method. Since the pure two-dimensional kagome antiferromagnet is most likely a magnetically disordered quantum spin liquid, we investigate the question whether the coupling of kagome layers in a stacked three-dimensional system may lead to a magnetically ordered ground state. We present spin-spin correlation functions and correlation lengths. For comparison we apply also linear spin wave theory. Our results provide strong evidence that the system remains short-range ordered independent of the sign and the strength of the interlayer coupling

Quasiperiodic Tip Splitting in Directional Solidification

We report experimental results on the tip splitting dynamics of seaweed growth in directional solidification of succinonitrile alloys with poly(ethylene oxide) or acetone as solutes. The seaweed or dense branching morphology was selected by solidifying grains which are oriented close to the {111} plane. Despite the random appearance of the growth, a quasiperiodic tip splitting morphology was observed in which the tip alternately splits to the left and to the right. The tip splitting frequency f was found to be related to the growth velocity V as a power law f V^{1.5}. This finding is consistent with the predictions of a tip splitting model that is also presented. Small anisotropies are shown to lead to different kinds of seaweed morphologies.Comment: 4 pages, 7 figures, submitted to Physical Review Letter