Penrose Matching Rules from Realistic Potentials in a Model System

We exhibit a toy model of a binary decagonal Al-Co quasicrystal -- closely related to actual structures -- in which realistic pair potentials yield a ground state which appears to perfectly implement Penrose's matching rules, for Hexagon-Boat-Star (HBS) tiles of edge 2.45 A. The second minimum of the potentials is crucial for this result.Comment: 7 pp, 2 figures; proc. "Quasicrystals: Silver Jubilee" (Tel Aviv, 2007), Phil. Mag. in pres

Combined energy -- diffraction data refinement of decagonal AlNiCo

We incorporate realistic pair potential energies directly into a non-linear least-square fit of diffraction data to quantitatively compare structure models with experiment for the Ni-rich $d$(AlNiCo) quasicrystal. The initial structure models are derived from a few {\it a priori} assumptions (gross features of the Patterson function) and the pair potentials. In place of the common hyperspace approach to the structure refinement of quasicrystals, we use a real-space tile decoration scheme, which does not rely on strict quasiperiodicity, and makes it easy to enforce sensible local arrangements of the atoms. Inclusion of the energies provides information complementary to the diffraction data and protects the fit procedure from converging on spurious solutions. The method pinpoints sites which are likely to break the symmetry of their local environment.Comment: 7 pages, 5 figures, proceedings of the Internation Conference on Quasicrystals, Bangalore, India, August 200

Synchronization and Coarsening (without SOC) in a Forest-Fire Model

We study the long-time dynamics of a forest-fire model with deterministic tree growth and instantaneous burning of entire forests by stochastic lightning strikes. Asymptotically the system organizes into a coarsening self-similar mosaic of synchronized patches within which trees regrow and burn simultaneously. We show that the average patch length grows linearly with time as t-->oo. The number density of patches of length L, N(L,t), scales as ^{-2}M(L/), and within a mean-field rate equation description we find that this scaling function decays as e^{-1/x} for x-->0, and as e^{-x} for x-->oo. In one dimension, we develop an event-driven cluster algorithm to study the asymptotic behavior of large systems. Our numerical results are consistent with mean-field predictions for patch coarsening.Comment: 5 pages, 4 figures, 2-column revtex format. To be submitted to PR

J1−J2J_1-J_2 quantum Heisenberg antiferromagnet on the triangular lattice: a group symmetry analysis of order by disorder

On the triangular lattice, for $J_2/J_1$ between $1/8$ and $1$, the classical Heisenberg model with first and second neighbor interactions presents four-sublattice ordered ground-states. Spin-wave calculations of Chubukov and Jolicoeur\cite{cj92} and Korshunov\cite{k93} suggest that quantum fluctuations select amongst these states a colinear two-sublattice order. From theoretical requirements, we develop the full symmetry analysis of the low lying levels of the spin-1/2 Hamiltonian in the hypotheses of either a four or a two-sublattice order. We show on the exact spectra of periodic samples ($N=12,16$ and $28$) how quantum fluctuations select the colinear order from the four-sublattice order.Comment: 15 pages, 4 figures (available upon request), Revte

Quasi-1D dynamics and nematic phases in the 2D Emery model

We consider the Emery model of a Cu-O plane of the high temperature superconductors. We show that in a strong-coupling limit, with strong Coulomb repulsions between electrons on nearest-neighbor O sites, the electron-dynamics is strictly one dimensional, and consequently a number of asymptotically exact results can be obtained concerning the electronic structure. In particular, we show that a nematic phase, which spontaneously breaks the point- group symmetry of the square lattice, is stable at low enough temperatures and strong enough coupling.Comment: 8 pages, 5 eps figures; revised manuscript with more detailed discussions; two new figures and three edited figuresedited figures; 14 references; new appendix with a detailed proof of the one-dimensional dynamics of the system in the strong coupling limi

Underlying Pairing States in Cuprate Superconductors

In this Letter, we develop a microscopic theory to describe the close proximity between the insulating antiferromagnetic (AF) order and the d-wave superconducting (dSC) order in cuprates. We show that the cuprate ground states form a configuration of coherent pairing states consisting of extended singlet Cooper pairs and triplet $\pi$ pairs, which can simultaneously describe AF and dSC orders.Comment: 4 papes, 1 figur

Surface Magnetization of Aperiodic Ising Quantum Chains

We study the surface magnetization of aperiodic Ising quantum chains. Using fermion techniques, exact results are obtained in the critical region for quasiperiodic sequences generated through an irrational number as well as for the automatic binary Thue-Morse sequence and its generalizations modulo p. The surface magnetization exponent keeps its Ising value, beta_s=1/2, for all the sequences studied. The critical amplitude of the surface magnetization depends on the strength of the modulation and also on the starting point of the chain along the aperiodic sequence.Comment: 11 pages, 6 eps-figures, Plain TeX, eps

Structure of the icosahedral Ti-Zr-Ni quasicrystal

The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined by invoking similarities to periodic crystalline phases, diffraction data and the results from ab initio calculations. The structure is modeled by decorations of the canonical cell tiling geometry. The initial decoration model is based on the structure of the Frank-Kasper phase W-TiZrNi, the 1/1 approximant structure of the quasicrystal. The decoration model is optimized using a new method of structural analysis combining a least-squares refinement of diffraction data with results from ab initio calculations. The resulting structural model of icosahedral Ti-Zr-Ni is interpreted as a simple decoration rule and structural details are discussed.Comment: 12 pages, 8 figure

The Kagome Antiferromagnet with Defects: Satisfaction, Frustration, and Spin Folding in a Random Spin System

It is shown that site disorder induces noncoplanar states, competing with the thermal selection of coplanar states, in the nearest neighbor, classical kagome Heisenberg antiferromagnet (AFM). For weak disorder, it is found that the ground state energy is the sum of energies of separately satisfied triangles of spins. This implies that disorder does not induce conventional spin glass behavior. A transformation is presented, mapping ground state spin configurations onto a folded triangular sheet (a new kind of ``spin origami'') which has conformations similar to those of tethered membranes.Comment: REVTEX, 11 pages + 3 pictures upon reques

Classical heisenberg antiferromagnet away from the pyrochlore lattice limit: entropic versus energetic selection

The stability of the disordered ground state of the classical Heisenberg pyrochlore antiferromagnet is studied within extensive Monte Carlo simulations by introducing an additional exchange interaction $J'$ that interpolates between the pyrochlore lattice ($J'=0$) and the face-centered cubic lattice ($J'=J$). It is found that for $J'/J$ as low as $J'/J\ge 0.01$, the system is long range ordered : the disordered ground state of the pyrochlore antiferromagnet is unstable when introducing very small deviations from the pure $J'=0$ limit. Furthermore, it is found that the selected phase is a collinear state energetically greater than the incommensurate phase suggested by a mean field analysis. To our knowledge this is the first example where entropic selection prevails over the energetic one.Comment: 5 (two-column revtex4) pages, 1 table, 7 ps/eps figures. Submitted to Phys. Rev.