arXiv subjects

R. Moessner

Publications and source records attributed to R. Moessner.

162 records · Page 9Linked to original sources

arXiv2000

Ising models of quantum frustration

We report on a systematic study of two dimensional, periodic, frustrated Ising models with a quantum dynamics introduced via a transverse magnetic field. The systems studied are the triangular and kagome lattice antiferromagnets, fully frustrated models on the square and hexagonal (honeycomb) lattices, a planar analog of the pyrochlore antiferromagnet, a pentagonal lattice antiferromagnet as well as a two quasi one-dimensional lattices that have considerable pedagogical value. All of these exhibit a macroscopic degeneracy at T=0 in the absence of the transverse field, which enters as a singular perturbation. We analyze these systems with a combination of a variational method at weak fields, a perturbative Landau-Ginzburg-Wilson (LGW) approach from large fields as well as quantum Monte Carlo simulations utilizing a cluster algorithm. Our results include instances of quantum order arising from classical criticality (triangular lattice) or classical disorder (pentagonal and probably hexagonal) as well as notable instances of quantum disorder arising from classical disorder (kagome). We also discuss the effect of a finite temperature, as well as the interplay between longitudinal and transverse fields--in the kagome problem the latter gives rise to a non-trivial phase diagram with bond-ordered and bond-critical phases in addition to the disordered phase. We also note connections to quantum dimer models and thereby to the physics of Heisenberg antiferromagnets in short-ranged resonating valence bond phases that have been invoked in discussions of high-temperature superconductivity.

cond-mat.stat-mech↗

arXiv2000

Magnets with strong geometric frustration

A non-technical introduction to the theory of magnets with strong geometric frustration is given, concentrating on magnets on corner-sharing (kagome, pyrochlore, SCGO and GGG) lattices. Their rich behaviour is traced back to a large ground-state degeneracy in model systems, which renders them highly unstable towards perturbations. A systematic classification according to properties of their ground states is discussed. Other topics addressed in this overview article include a general theoretical framework for thermal order by disorder; the dynamics of how the vast regions of phase space accessible at low temperature are explored; the origin of the featureless magnetic susceptibility fingerprint of geometric frustration; the role of perturbations; and spin ice. The rich field of quantum frustrated magnets is also touched on.

cond-mat.stat-mech↗

arXiv2000

An RVB phase in the triangular lattice quantum dimer model

We study the quantum dimer model on the triangular lattice, which is expected to describe the singlet dynamics of frustrated Heisenberg models in phases where valence bond configurations dominate their physics. We find, in contrast to the square lattice, that there is a truly short ranged resonating valence bond (RVB) phase with no gapless collective excitations and with deconfined, gapped, spinons for a {\it finite} range of parameters. We also establish the presence of three crystalline phases in this system.

cond-mat.str-el↗

arXiv2000

Frustrated Order by Disorder: the Pyrochlore Antiferromagnet with Bond Disorder

The classical Heisenberg antiferromagnet on the pyrochlore lattice is macroscopically and continuously degenerate and the system remains disordered at all temperatures, even in the presence of weak dilution with nonmagnetic ions. We show that, in stark contrast, weak bond disorder lifts the ground state degeneracy in favour of locally collinear spin configurations. We present a proof that for a single tetrahedron the ground state is perfectly collinear but identify two mechanisms which preclude the establishment of a globally collinear state; one due to frustration and the other due to higher-order effects. We thus obtain a rugged energy landscape, which is necessary to account for the glassy phenomena found in real systems such as the pyrochlore Y_2Mo_2O_7 recently reported by Booth et al. [Booth] to contain a substantial degree of bond disorder.

cond-mat.dis-nn↗

arXiv2000

Slow holes in the triangular Ising antiferromagnet

We consider the problem of the doped Ising antiferromagnet on the frustrated triangular lattice in the limit where the hole kinetic energy is much smaller than the Ising exchange. For a {\it single} hole we prove a ``frustrated Nagaoka theorem'' showing that the ground state is magnetized and breaks translational symmetry, in contrast to the parent insulating state that is unmagnetized and spatially homogenous. The extension of this physics to finite dopings depends on the strength of a density-density coupling that is inevitably present - we find either phase separation of the holes, or a superconducting state that is {\it also} magnetized and breaks translational symmetry in a feat of spatial self-organization. Finally, we derive an effective interaction between dilute holes at temperatures in excess of the hopping and find an oscillatory, long-ranged form reflective of the correlations in the underlying classical magnet which presages the breaking of translational symmetry at zero temperature.

cond-mat.str-el↗

arXiv2000

Two-dimensional periodic frustrated Ising models in a transverse field

We investigate the interplay of classical degeneracy and quantum dynamics in a range of periodic frustrated transverse field Ising systems at zero temperature. We find that such dynamics can lead to unusual ordered phases and phase transitions, or to a quantum spin liquid (cooperative paramagnetic) phase as in the triangular and kagome lattice antiferromagnets, respectively. For the latter, we further predict passage to a bond-ordered phase followed by a critical phase as the field is tilted. These systems also provide exact realizations of quantum dimer models introduced in studies of high temperature superconductivity.

cond-mat.stat-mech↗

arXiv1999

Magnetic susceptibility of diluted pyrochlore and SCGO antiferromagnets

We investigate the magnetic susceptibility of the classical Heisenberg antiferromagnet with nearest-neighbour interactions on the geometrically frustrated pyrochlore lattice, for a pure system and in the presence of dilution with nonmagnetic ions. Using the fact that the correlation length in this system for small dilution is always short, we obtain an approximate but accurate expression for the magnetic susceptibility at all temperatures. We extend this theory to the compound SrCr_{9-9x}Ga_{3+9x}O_{19} (SCGO) and provide an explanation of the phenomenological model recently proposed by Schiffer and Daruka [Phys. Rev. B56, 13712 (1997)].

cond-mat.stat-mech↗

arXiv1998

Angular Cross-Correlation of Galaxies: A Probe of Gravitational Lensing by Large-Scale Structure

The angular cross-correlation between two galaxy samples separated in redshift is shown to be a useful measure of weak lensing by large-scale structure. Angular correlations in faint galaxies arise due to spatial clustering of the galaxies as well as gravitational lensing by dark matter along the line-of-sight. The lensing contribution to the 2-point auto-correlation function is typically small compared to the gravitational clustering. However the cross-correlation between two galaxy samples is nearly unaffected by gravitational clustering provided their redshift distributions do not overlap. The cross-correlation is then induced by magnification bias due to lensing by large-scale structure. We compute the expected amplitude of the cross-correlation for popular theoretical models of structure formation. For two populations with mean redshifts of $\simeq 0.3$ and 1, we find a cross-correlation signal of $\simeq 1%$ on arcminute scales and $\simeq 3%$ on a few arcseconds. The dependence on the cosmological parameters $Ω$ and $Λ$, on the dark matter power spectrum and on the bias factor of the foreground galaxy population is explored.

astro-ph↗

arXiv1998

Low-temperature properties of classical, geometrically frustrated antiferromagnets

We study the ground-state and low-energy properties of classical vector spin models with nearest-neighbour antiferromagnetic interactions on a class of geometrically frustrated lattices which includes the kagome and pyrochlore lattices. We explore the behaviour of these magnets that results from their large ground-state degeneracies, emphasising universal features and systematic differences between individual models. We investigate the circumstances under which thermal fluctuations select a particular subset of the ground states, and find that this happens only for the models with the smallest ground-state degeneracies. For the pyrochlore magnets, we give an explicit construction of all ground states, and show that they are not separated by internal energy barriers. We study the precessional spin dynamics of the Heisenberg pyrochlore antiferromagnet. There is no freezing transition or selection of preferred states. Instead, the relaxation time at low temperature, T, is of order hbar/(k_B T). We argue that this behaviour can also be expected in some other systems, including the Heisenberg model for the compound SrCr_8Ga_4O_{19}.

cond-mat.stat-mech↗

arXiv1997

Properties of a classical spin liquid: the Heisenberg pyrochlore antiferromagnet

We study the low-temperature behaviour of the classical Heisenberg antiferromagnet with nearest neighbour interactions on the pyrochlore lattice. Because of geometrical frustration, the ground state of this model has an extensive number of degrees of freedom. We show, by analysing the effects of small fluctuations around the ground-state manifold, and from the results of Monte Carlo and molecular dynamics simulations, that the system is disordered at all temperatures, T, and has a finite relaxation time, which varies as 1/T for small T.

cond-mat.stat-mech↗

arXiv1997

Expansions for nearly Gaussian distributions

Various types of expansions in series of Chebyshev-Hermite polynomials currently used in astrophysics for weakly non-normal distributions are compared, namely the Gram-Charlier, Gauss-Hermite and Edgeworth expansions. It is shown that the Gram-Charlier series is most suspect because of its poor convergence properties. The Gauss-Hermite expansion is better but it has no intrinsic measure of accuracy. The best results are achieved with the asymptotic Edgeworth expansion. We draw attention to the form of this expansion found by Petrov for arbitrary order of the asymptotic parameter and present a simple algorithm realizing Petrov's prescription for the Edgeworth expansion. The results are illustrated by examples similar to the problems arising when fitting spectral line profiles of galaxies, supernovae, or other stars, and for the case of approximating the probability distribution of peculiar velocities in the cosmic string model of structure formation.

astro-ph↗

arXiv1997

The Effect of Weak Lensing on the Angular Correlation Function of Faint Galaxies

The angular correlation function \wth of faint galaxies is affected both by nonlinear gravitational evolution and by magnification bias due to gravitational lensing. We compute the resulting \wth for different cosmological models and show how its shape and redshift evolution depend on Ωand Λ. For galaxies at redshift greater than 1 (R magnitude fainter than about 24), magnification bias can significantly enhance or suppress \wth, depending on the slope of the number-magnitude relation. We show for example how it changes the ratio of \wth for two galaxy samples with different number-count slopes.

astro-ph↗

arXiv1997

Early Objects in the Cosmic String Theory with Hot Dark Matter

We study the accretion of hot dark matter onto moving cosmic string loops, using an adaptation of the Zeldovich approximation to HDM. We show that a large number of nonlinear objects of mass greater than $10^{12}M_\odot$, which could be the hosts of high redshift quasars, are formed by a redshift of $z=4$.

astro-ph↗

arXiv1996

Exact results for interacting electrons in high Landau levels

We study a two-dimensional electron system in a magnetic field with a fermion hardcore interaction and without disorder. Projecting the Hamiltonian onto the n-th Landau level, we show that the Hartree-Fock theory is exact in the limit n \rightarrow \infty, for the high temperature, uniform density phase of an infinite system; for a finite-size system, it is exact at all temperatures. In addition, we show that a charge-density wave arises below a transition temperature T_t. Using Landau theory, we construct a phase diagram which contains both unidirectional and triangular charge-density wave phases. We discuss the unidirectional charge-density wave at zero temperature and argue that quantum fluctuations are unimportant in the large-n limit. Finally, we discuss the accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction.

cond-mat↗

arXiv1995

Formation of High Redshift Objects in a Cosmic String Theory with Hot Dark Matter

Using a modification of the Zel'dovich approximation adapted to hot dark matter, the accretion of such matter onto moving cosmic string loops is studied. It is shown that a large number of $10^{12}M_\odot$ nonlinear objects will be produced by a redshift of $z=4$. These objects could be the hosts of high redshift quasars.

astro-ph↗

arXiv1995

Statistics of Peculiar Velocities from Cosmic Strings

We calculate the probability distribution of a single component of peculiar velocities due to cosmic strings, smoothed over regions with a radius of several $h^{-1}$ Mpc. The probability distribution is shown to be Gaussian to good accuracy, in agreement with the distribution of peculiar velocities deduced from the 1.9 Jy IRAS redshift survey. Using the normalization of parameters of the cosmic string model from CMB measurements, we show that the rms values for peculiar velocities inferred from IRAS are consistent with the cosmic string model provided that long strings have some small-scale structure.

astro-ph↗

arXiv1994

Singularity-Free Two Dimensional Cosmologies

We present a class of theories of two dimensional gravity which admits homogeneous and isotropic solutions that are nonsingular and asymptotically approach a FRW matter dominated universe at late times. These models are generalizations of two dimensional dilaton gravity and both vacuum solutions and those including conformally coupled matter are investigated. In each case our construction leads to an inflationary stage driven by the gravitational sector. Our work comprises a simple example of the `Nonsingular Universe' constructions of ref. [1].

gr-qc↗

arXiv1993

A Cosmic String Specific Signature on the Cosmic Microwave Background

Using an analytical model for the string network we show that the kurtosis of cosmic microwave background (CMB) temperature gradient maps is a good statistic to distinguish between the cosmic string model and inflationary models of structure formation. The difference between the stringy and inflationary value for the kurtosis is inversely proportional to the angular resolution and to the number of strings per Hubble volume of the strings' scaling solution. If strings are indeed responsible for CMB anisotropies then experiments with resolutions of a couple of arcminutes or smaller could determine it using this statistic.

astro-ph↗