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, \xi, is introduced with a small magnetic field, h, and an accurate expression for \xi(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.Comment: 7 pages, 4 figures, 1 table. To appear in Phys. Rev.

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.Comment: 15 pages, including 7 ps figure

Comment on "Short-range magnetic interactions in the spin-ice compound Ho2Ti2O7"

In their recent communication (Phys. Rev. B 64, 060406(R) (2001)) Cornelius and Gardner have reported the results of magnetization and susceptibility studies on single crystals of the pyrochlore Ho2Ti2O7. The observed field dependence of magnetization is totally unexpected, as it seems to suggest that the magnetic moments in this compound do not obey the 'ice-rule'. We have re-measured the magnetization curves for Ho2Ti2O7 single crystal for the three principal directions of an applied magnetic field and found nearly perfect agreement with the predictions for a nearest-neighbor spin-ice model.Comment: comment on Phys. Rev. B 64, 060406(R) (2001

Finite size scaling in the 2D XY-model and generalized universality

In recent works (BHP), a generalized universality has been proposed, linking phenomena as dissimilar as 2D magnetism and turbulence. To test these ideas, we performed a MC study of the 2D XY-model. We found that the shape of the probability distribution function for the magnetization M is non Gaussian and independent of the system size --in the range of the lattice sizes studied-- below the Kosterlitz-Thoules temperature. However, the shape of these distributions does depend on the temperature, contrarily to the BHP's claim. This behavior is successfully explained by using an extended finite-size scaling analysis and the existence of bounds for M.Comment: 7 pages, 5 figures. Submitted to Phys. Rev. Lett. Details of changes: 1. We emphasized in the abstract the range of validity of our results. 2. In the last paragraph the temperature dependence of the PDF was slightly re-formulate

Understanding Paramagnetic Spin Correlations in the Spin-Liquid Pyrochlore Tb2Ti2O7

Recent elastic and inelastic neutron scattering studies of the highly frustrated pyrochlore antiferromagnet Tb2Ti2O7 have shown some very intriguing features that cannot be modeled by the local classical Ising model, naively expected to describe this system at low temperatures. Using the random phase approximation to take into account fluctuations between the ground state doublet and the first excited doublet, we successfully describe the elastic neutron scattering pattern and dispersion relations in Tb2Ti2O7, semi-quantitatively consistent with experimental observations.Comment: revtex4, 4 pages, 1 Color+ 2 BW figure

About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass

Recently, it has been conjectured that the statistics of extremes is of relevance for a large class of correlated system. For certain probability densities this predicts the characteristic large $x$ fall-off behavior $f(x)\sim\exp (-a e^x)$, $a>0$. Using a multicanonical Monte Carlo technique, we have calculated the Parisi overlap distribution $P(q)$ for the three-dimensional Edward-Anderson Ising spin glass at and below the critical temperature, even where $P(q)$ is exponentially small. We find that a probability distribution related to extreme order statistics gives an excellent description of $P(q)$ over about 80 orders of magnitude.Comment: 4 pages RevTex, 3 figure

Overlap Distribution of the Three-Dimensional Ising Model

We study the Parisi overlap probability density P_L(q) for the three-dimensional Ising ferromagnet by means of Monte Carlo (MC) simulations. At the critical point P_L(q) is peaked around q=0 in contrast with the double peaked magnetic probability density. We give particular attention to the tails of the overlap distribution at the critical point, which we control over up to 500 orders of magnitude by using the multi-overlap MC algorithm. Below the critical temperature interface tension estimates from the overlap probability density are given and their approach to the infinite volume limit appears to be smoother than for estimates from the magnetization.Comment: 7 pages, RevTex, 9 Postscript figure

Persistent global power fluctuations near a dynamic transition in electroconvection

This is a study of the global fluctuations in power dissipation and light transmission through a liquid crystal just above the onset of electroconvection. The source of the fluctuations is found to be the creation and annihilation of defects. They are spatially uncorrelated and yet temporally correlated. The temporal correlation is seen to persist for extremely long times. There seems to be an especially close relation between defect creation/annihilat ion in electroconvection and thermal plumes in Rayleigh-B\'enard convection

Roughness distributions for 1/f^alpha signals

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions, distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also non-periodic signals on short intervals embedded in the full period. We find that for alpha=<1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for alpha>1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha=2 and alpha->infinity. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f^alpha processes.Comment: 12 pages incl. 6 figures, with RevTex4, for A4 paper, in v2 some references were correcte

Anisotropic Release of the Residual Zero-point Entropy in the Spin Ice Compound Dy2Ti2O7: Kagome-ice Behavior

We report the specific heat and entropy of single crystals of the spin ice compound Dy2Ti2O7 at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions: [100], [110], [111] and [112]. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches Rln2. However, in the intermediate field region, the entropy in fields along the [111] direction is different from those for the other three field directions. For the [111] direction the frustration structure changes from that of three-dimensional(3D) pyrochlore to that of two-dimensional(2D) Kagome-like lattice with constraint due to the ice rule, leading to different values of zero-point entropy.Comment: 4 pages, 4 figures, to appear in Phys. Rev.