Temperature-dependent "phason" elasticity in a random tiling quasicrystal

Both ``phason'' elastic constants have been measured from Monte Carlo simulations of a random-tiling icosahedral quasicrystal model with a Hamiltonian. The low-temperature limit approximates the ``canonical-cell'' tiling used to describe several real quasicrystals. The elastic constant K2 changes sign from positive to negative with decreasing temperature; in the ``canonical-cell'' limit, K2/K1 appears to approach -0.7, about the critical value for a phason-mode modulation instability. We compare to the experiments on i-AlPdMn and i-AlCuFe.Comment: 5 pages, 2 Postscript figures, LaTeX, uses revtex4, submitted to PR

First-principles prediction of a decagonal quasicrystal containing boron

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants. These approximant structures imply a deterministic decoration of tiles by atoms that can be extended quasiperiodically. Experimentally observed structural disorder corresponds to phason (tile flip) fluctuations. First-principles total energy calculations reveal that many distinct tilings lie close to stability at low temperatures. Transfer matrix calculations based on these energies suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B$_{38}$Mg$_{17}$Ru$_{45}$ forms a decagonal quasicrystal that is metastable at low temperatures and may be thermodynamically stable at high temperatures.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Depleted pyrochlore antiferromagnets

I consider the class of "depleted pyrochlore" lattices of corner-sharing triangles, made by removing spins from a pyrochlore lattice such that every tetrahedron loses exactly one. Previously known examples are the "hyperkagome" and "kagome staircase". I give criteria in terms of loops for whether a given depleted lattice can order analogous to the kagome \sqrt{3} \times \sqrt{three} state, and also show how the pseudo-dipolar correlations (due to local constraints) generalize to even the random depleted case.Comment: 6pp IOP latex, 1 figure; Proc. "Highly Frustrated Magnetism 2008", Sept 2008, Braunschwei

Effective Hamiltonian and low-lying energy clustering patterns of four-sublattice antiferromagnets

We study the low-lying energy clustering patterns of quantum antiferromagnets with p sublattices (in particular p=4). We treat each sublattice as a large spin, and using second-order degenerate perturbation theory, we derive the effective (biquadratic) Hamiltonian coupling the p large spins. In order to compare with exact diagonalizations, the Hamiltonian is explicitly written for a finite-size lattice, and it contains information on energies of excited states as well as the ground state. The result is applied to the face-centered-cubic Type I antiferromagnet of spin 1/2, including second-neighbor interactions. A 32-site system is exactly diagonalized, and the energy spectrum of the low-lying singlets follows the analytically predicted clustering pattern.Comment: 17 pages, 4 table

Spontaneous Currents in Spinless Fermion Lattice Models at the Strong-Coupling Limit

What kind of lattice Hamiltonian manifestly has an ordered state with spontaneous orbital currents? We consider interacting spinless fermions on an array of square plaquettes, connected by weak hopping; the array geometry may be a 2 x 2L ladder, a 2 x 2 x 2L "tube", or a 2L x 2L square grid. At half filling, we derive an effective Hamiltonian in terms of pseudospins, of which one component represents orbital currents, and find the conditions sufficient for orbital current long-range order. We consider spinfull variants of the aforesaid spinless models and make contact with other spinfull models in the literature purported to possess spontaneous currents.Comment: added two new references following recent communicatio

Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions

By removing one empty site between two occupied sites, we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest-neighbor repulsion respectively, and ultimately in terms of the one-dimensional Fermi sea. We then introduce the intervening-particle expansion, where we write correlation functions in such ground states as a systematic sum over conditional expectations, each of which can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various ground-state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest-neighbor repulsion, as well as for a ladder model of spinless fermions with infinite nearest-neighbor repulsion and correlated hopping in three limiting cases. We find that the decay of these correlation functions are governed by surprising power-law exponents.Comment: 20 pages, 18 figures, RevTeX4 clas

Intercept Surveys: An Overlooked Method for Data Collection

Intercept surveys are a tool Extension educators can use to capture local data quickly and with minimal cost. We used intercept surveys at city farmers\u27 markets to test the efficacy of food safety signage. From our experience with the intercept survey process, we identified a set of best practices that can benefit other Extension educators interested in developing and implementing this type of research

Phason elasticity of a three-dimensional quasicrystal: transfer-matrix method

We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these models, which are related to experimental measurables such as phason Debye-Waller factors, and diffuse scattering wings near Bragg peaks. We apply our method to the canonical-cell model of the icosahedral phase, making use of results from a previously-presented calculation in which the possible structures for this model under specific periodic boundary conditions were cataloged using a computational technique. We give results for the configurational entropy density and the two fundamental elastic constants for a range of system sizes. The method is general enough allow a similar calculation to be performed for any other random tiling model.Comment: 38 pages, 3 PostScript figures, self-expanding uuencoded compressed tar file, LaTeX using RevTeX macros and epsfig.st

Effect of Quantum Fluctuations on Magnetic Ordering in CaV3_3O7_7

We present a theoretical model for CaV$_3$O$_7$: the $1/4$-depleted square spin-$1/2$ Heisenberg model which includes both the nearest-neighbor coupling ($J$) and the next-nearest-neighbor coupling ($J'$), where $J$ and $J'$ are antiferromagnetic. Recent experiments of the neutron diffraction by Harashina et.al. report the magnetic ordering at low temperatures, which may be called as a stripe phase. It is shown that the observed spin structure is not stable in the classical theory. By employing the modified spin wave theory, we show that the stripe phase is stabilized by the quantum fluctuations for $J'/J > 0.69$. In CaV$_3$O$_7$, the coupling constants are estimated as $J \sim J'$ by comparing the theoretical and experimental results.Comment: submitted to J. Phys. Soc. Jp