Method of fabricating an object with a thin wall having a precisely shaped slit

A method is described for making a structure with a cavity and a thin wall with a precisely shaped slit. An object with a cavity having two openings, one of which is to be closed by a thin wall with a slit, is placed on the surface of a fixture. The fixture surface has a slot conforming to the size and shape of the slit to be formed in the thin wall

Bethe Ansatz solution of a decagonal rectangle triangle random tiling

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.Comment: 17 pages, 4 figures, some remarks added and typos correcte

Valence-bond crystal in a {111} slice of the pyrochlore antiferromagnet

We investigate theoretically the ordering effect of quantum spin fluctuations in a Heisenberg antiferromagnet on a two-dimensional network of corner sharing tetrahedra. This network is obtained as a {111} slice of the highly frustrated pyrochlore lattice, from which it inherits the equivalence of all three pairs of opposite bonds of each tetrahedron. The lowest-order (in 1/S) quantum corrections partially lift the huge degeneracy of the classical ground state and select an ensemble of states with long-range valence-bond order.Comment: 4 pages, 2 EPS figures. Minor revision: clarifications in response to referee comments, additional reference

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

Power-law spin correlations in pyrochlore antiferromagnets

The ground state ensemble of the highly frustrated pyrochlore-lattice antiferromagnet can be mapped to a coarse-grained ``polarization'' field satisfying a zero-divergence condition From this it follows that the correlations of this field, as well as the actual spin correlations, decay with separation like a dipole-dipole interaction ($1/|R|^3$). Furthermore, a lattice version of the derivation gives an approximate formula for spin correlations, with several features that agree well with simulations and neutron-diffraction measurements of diffuse scattering, in particular the pinch-point (pseudo-dipolar) singularities at reciprocal lattice vectors. This system is compared to others in which constraints also imply diffraction singularities, and other possible applications of the coarse-grained polarization are discussed.Comment: 13 pp, revtex, two figure

Quantum spin liquids: a large-S route

This paper explores the large-S route to quantum disorder in the Heisenberg antiferromagnet on the pyrochlore lattice and its homologues in lower dimensions. It is shown that zero-point fluctuations of spins shape up a valence-bond solid at low temperatures for one two-dimensional lattice and a liquid with very short-range valence-bond correlations for another. A one-dimensional model demonstrates potential significance of quantum interference effects (as in Haldane's gap): the quantum melting of a valence-bond order yields different valence-bond liquids for integer and half-integer values of S.Comment: Proceedings of Highly Frustrated Magnetism 2003 (Grenoble), 6 LaTeX page

Isospin symmetry breaking in an algebraic pairing Sp(4) model

An exactly solvable sp(4) algebraic approach extends beyond the traditional isospin conserving nuclear interaction to bring forward effects of isospin symmetry breaking and isospin mixing resulting from a two-body nuclear interaction that includes proton-neutron (pn) and like-particle isovector pairing correlations plus significant isoscalar pn interactions. The model yields an estimate for the extent to which isobaric analog 0+ states in light and medium mass nuclei may mix with one another and reveals possible, but still extremely weak, non-analog beta-decay transitions.Comment: 8 pages, 2 figure

Heisenberg antiferromagnet on Cayley trees: low-energy spectrum and even/odd site imbalance

To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being "giant spins" arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.Comment: 19 pages, 12 figures, 6 tables. Changes made to manuscript after referee suggestions: parts reorganized, clarified discussion on Fibonacci tree, typos correcte

Scaling laws and simulation results for the self--organized critical forest--fire model

We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer simulations in 1 to 8 dimensions. The simulations suggest a critical dimension $d_c=6$ above which the critical exponents assume their mean--field values. Changing the lattice symmetry and allowing trees to be immune against fire, we show that the critical exponents are universal.Comment: 12 pages, postscript uuencoded, figures included, to appear in Phys. Rev.