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P. C. W. Holdsworth

Publications and source records attributed to P. C. W. Holdsworth.

33 records · Page 2Linked to original sources
arXiv2005

Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order

We study the ground state properties of a quantum antiferromagnet on the kagome lattice in the presence of a magnetic field, paying particular attention to the stability of the plateau at magnetization 1/3 of saturation and the nature of its ground state. We discuss fluctuations around classical ground states and argue that quantum and classical calculations at the harmonic level do not lead to the same result in contrast to the zero-field case. For spin S=1/2 we find a magnetic gap below which an exponential number of non-magnetic excitations are present. Moreover, such non-magnetic excitations also have a (much smaller) gap above the three-fold degenerate ground state. We provide evidence that the ground state has long-range order of valence-bond crystal type with nine spins in the unit cell.

cond-mat.str-el↗
arXiv2004

Ground state and low-lying excitations of the spin-1/2 XXZ model on the kagome lattice at magnetization 1/3

We study the ground state and low-lying excitations of the S=1/2 XXZ antiferromagnet on the kagome lattice at magnetization one third of the saturation. An exponential number of non-magnetic states is found below a magnetic gap. The non-magnetic excitations also have a gap above the ground state, but it is much smaller than the magnetic gap. This ground state corresponds to an ordered pattern with resonances in one third of the hexagons. The spin-spin correlation function is short ranged, but there is long-range order of valence-bond crystal type.

cond-mat.str-el↗
arXiv2003

Statistics of extremal intensities for Gaussian interfaces

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e. roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases: (i) in the non-dispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in novel scenarios.

cond-mat.stat-mech↗
arXiv2003

Er2Ti2O7: Evidence of Order by Disorder in a Frustrated Antiferromagnet

Er_2Ti_2O_7 has been suggested to be a realization of the frustrated < 111 > XY pyrochlore lattice antiferromagnet, for which theory predicts fluctuation-induced symmetry breaking in a highly degenerate ground state manifold. We present a theoretical analysis of the classical model compared to neutron scattering experiments on the real material, both below and above T_N = 1.173(2) K. The model correctly predicts the ordered magnetic structure, suggesting that the real system has order stabilised by zero-point quantum fluctuations that can be modelled by classical spin wave theory. However, the model fails to describe the excitations of the system, which show unusual features.

cond-mat↗
arXiv2003

Intermittency and non-Gaussian fluctuations of the global energy transfer in fully developed turbulence

We address the experimentally observed non-Gaussian fluctuations for the energy injected into a closed turbulent flow at fixed Reynolds number. We propose that the power fluctuations mirror the internal kinetic energy fluctuations. Using a stochastic cascade model, we construct the excess kinetic energy as the sum over the energy transfers at different levels of the cascade. We find an asymmetric distribution that strongly resembles the experimental data. The asymmetry is an explicit consequence of intermittency and the global measure is dominated by small scale events correlated over the entire system. Our calculation is consistent with the statistical analogy recently made between a confined turbulent flow and a critical system of finite size.

cond-mat.stat-mech↗
arXiv2001

From classical to quantum Kagome antiferromagnet in a magnetic field

We study the magnetic properties of the Kagome antiferromagnet going from the classical limit to the deep quantum regime of spin 1/2 systems. In all the cases there are special values for the magnetization, 1/3 in particular, in which a singular behavior is observed to occur in both the classical and quantum cases. We show clear evidence for a magnetization plateau for the spin 1/2 case in a wide range of XXZ anisotropies and for the occurrence of quantum order by disorder effects.

cond-mat.str-el↗
arXiv2001

Reply to Comment on "Universal Fluctuations in Correlated Systems", by B. Zheng and S. Trimper, cond-mat/0109003

We reply to the comment on our published paper `` Universal Fluctuations in Correlated Systems'',Phys. Rev. Lett. Vol; 84, p3744 (2000), by B. Zheng and S. Trimper, cond-mat/0109003. We argue that their results confirm our conjecture, that the probability distribution for order parameter fluctuations in the 2D and 3D Ising models at a temperature $T^{\ast}(L)$ slightly below $T_C$ for the infinite, system approximates the universal functional form of the 2D-XY model in its low temperature phase. We discuss the relevance of the temperature interval $T_C-T^{\ast}$, considered to be large by Zheng and Trimper and explain why the observed phenomena is a critical phenomena.

cond-mat.stat-mech↗
arXiv2001

Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model

We analyse the spin wave approximation for the 2D-XY model, directly in reciprocal space. In this limit the model is diagonal and the normal modes are statistically independent. Despite this simplicity non-trivial critical properties are observed and exploited. We confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the Brillouin zone. We show that the asymmetry is a many body effect despite the importance played by the zone centre. The precise form of the function is dependent on the details of the Gibbs measure, giving weight to the idea that an effective Gibbs measure should exist in non-equilibrium systems, if a similar distribution is observed.

cond-mat.stat-mech↗
arXiv2001

Universal Magnetic Fluctuations with a Field Induced Length Scale

We calculate the probability density function for the order parameter fluctuations in the low temperature phase of the 2D-XY model of magnetism near the line of critical points. A finite correlation length, ξ, is introduced with a small magnetic field, h, and an accurate expression for ξ(h) is developed by treating non-linear contributions to the field energy using a Hartree approximation. We find analytically a series of universal non-Gaussian distributions with a finite size scaling form and present a Gumbel-like function that gives the PDF to an excellent approximation. We propose the Gumbel exponent, a(h), as an indirect measure of the length scale of correlations in a wide range of complex systems.

cond-mat.stat-mech↗
arXiv2001

Competition Between Exchange and Anisotropy in a Pyrochlore Ferromagnet

The Ising-like spin ice model, with a macroscopically degenerate ground state, has been shown to be approximated by several real materials. Here we investigate a model related to spin ice, in which the Ising spins are replaced by classical Heisenberg spins. These populate a cubic pyrochlore lattice and are coupled to nearest neighbours by a ferromagnetic exchange term J and to the local <1,1,1> axes by a single-ion anisotropy term D. The near neighbour spin ice model corresponds to the case D/J infinite. For finite D/J we find that the macroscopic degeneracy of spin ice is broken and the ground state is magnetically ordered into a four-sublattice structure. The transition to this state is first-order for D/J > 5 and second-order for D/J < 5 with the two regions separated by a tricritical point. We investigate the magnetic phase diagram with an applied field along [1,0,0] and show that it can be considered analogous to that of a ferroelectric.

cond-mat.stat-mech↗
arXiv2000

Magnetic fluctuations in the classical XY model: the origin of an exponential tail in a complex system

We study the probability density function for the fluctuations of the magnetic order parameter in the low temperature phase of the XY model of finite size. In two-dimensions this system is critical over the whole of the low temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent $η$. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high resolution molecular dynamics and Monte Carlo simulations. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than four, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behaviour observed in models of interface growth and for dissipative systems driven into a non-equilibrium steady state.

cond-mat.stat-mech↗
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↗
arXiv1999

Universal Fluctuations in Correlated Systems

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D-XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated, equilibrium and non-equilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sand-piles, avalanches and granular media in a self organized critical state. We discuss the relationship with both Gaussian and extremal statistics.

cond-mat.stat-mech↗
arXiv1993

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.

cond-mat↗