Strong universality and algebraic scaling in two-dimensional Ising spin glasses

At zero temperature, two-dimensional Ising spin glasses are known to fall into several universality classes. Here we consider the scaling at low but non-zero temperature and provide numerical evidence that $\eta \approx 0$ and $\nu \approx 3.5$ in all cases, suggesting a unique universality class. This algebraic (as opposed to exponential) scaling holds in particular for the $\pm J$ model, with or without dilutions and for the plaquette diluted model. Such a picture, associated with an exceptional behavior at T=0, is consistent with a real space renormalization group approach. We also explain how the scaling of the specific heat is compatible with the hyperscaling prediction

Finite size scaling in Villain's fully frustrated model and singular effects of plaquette disorder

The ground state and low T behavior of two-dimensional spin systems with discrete binary couplings are subtle but can be analyzed using exact computations of finite volume partition functions. We first apply this approach to Villain's fully frustrated model, unveiling an unexpected finite size scaling law. Then we show that the introduction of even a small amount of disorder on the plaquettes dramatically changes the scaling laws associated with the T=0 critical point.Comment: Latex with 3 ps figures. Last versio

Domain wall entropy of the bimodal two-dimensional Ising spin glass

We report calculations of the domain wall entropy for the bimodal two-dimensional Ising spin glass in the critical ground state. The L * L system sizes are large with L up to 256. We find that it is possible to fit the variance of the domain wall entropy to a power function of L. However, the quality of the data distributions are unsatisfactory with large L > 96. Consequently, it is not possible to reliably determine the fractal dimension of the domain walls.Comment: 4 pages, 2 figures, submitted to PR

Genome-wide association study of behavioural and psychiatric features in human prion disease.

Prion diseases are rare neurodegenerative conditions causing highly variable clinical syndromes, which often include prominent neuropsychiatric symptoms. We have recently carried out a clinical study of behavioural and psychiatric symptoms in a large prospective cohort of patients with prion disease in the United Kingdom, allowing us to operationalise specific behavioural/psychiatric phenotypes as traits in human prion disease. Here, we report exploratory genome-wide association analysis on 170 of these patients and 5200 UK controls, looking for single-nucleotide polymorphisms (SNPs) associated with three behavioural/psychiatric phenotypes in the context of prion disease. We also specifically examined a selection of candidate SNPs that have shown genome-wide association with psychiatric conditions in previously published studies, and the codon 129 polymorphism of the prion protein gene, which is known to modify various aspects of the phenotype of prion disease. No SNPs reached genome-wide significance, and there was no evidence of altered burden of known psychiatric risk alleles in relevant prion cases. SNPs showing suggestive evidence of association (P<10(-5)) included several lying near genes previously implicated in association studies of other psychiatric and neurodegenerative diseases. These include ANK3, SORL1 and a region of chromosome 6p containing several genes implicated in schizophrenia and bipolar disorder. We would encourage others to acquire phenotype data in independent cohorts of patients with prion disease as well as other neurodegenerative and neuropsychiatric conditions, to allow meta-analysis that may shed clearer light on the biological basis of these complex disease manifestations, and the diseases themselves

Critical thermodynamics of the two-dimensional +/-J Ising spin glass

We compute the exact partition function of 2d Ising spin glasses with binary couplings. In these systems, the ground state is highly degenerate and is separated from the first excited state by a gap of size 4J. Nevertheless, we find that the low temperature specific heat density scales as exp(-2J/T), corresponding to an ``effective'' gap of size 2J; in addition, an associated cross-over length scale grows as exp(J/T). We justify these scalings via the degeneracy of the low-lying excitations and by the way low energy domain walls proliferate in this model

Energy gap of the bimodal two-dimensional Ising spin glass

An exact algorithm is used to compute the degeneracies of the excited states of the bimodal Ising spin glass in two dimensions. It is found that the specific heat at arbitrary low temperature is not a self-averaging quantity and has a distribution that is neither normal or lognormal. Nevertheless, it is possible to estimate the most likely value and this is found to scale as L^3 T^(-2) exp(-4J/kT), for a L*L lattice. Our analysis also explains, for the first time, why a correlation length \xi ~ exp(2J/kT) is consistent with an energy gap of 2J. Our method allows us to obtain results for up to 10^5 disorder realizations with L <= 64. Distributions of second and third excitations are also shown.Comment: 4 pages, 4 figure

Pointwise consistency of the kriging predictor with known mean and covariance functions

This paper deals with several issues related to the pointwise consistency of the kriging predictor when the mean and the covariance functions are known. These questions are of general importance in the context of computer experiments. The analysis is based on the properties of approximations in reproducing kernel Hilbert spaces. We fix an erroneous claim of Yakowitz and Szidarovszky (J. Multivariate Analysis, 1985) that the kriging predictor is pointwise consistent for all continuous sample paths under some assumptions.Comment: Submitted to mODa9 (the Model-Oriented Data Analysis and Optimum Design Conference), 14th-19th June 2010, Bertinoro, Ital

Large random correlations in individual mean field spin glass samples

We argue that complex systems must possess long range correlations and illustrate this idea on the example of the mean field spin glass model. Defined on the complete graph, this model has no genuine concept of distance, but the long range character of correlations is translated into a broad distribution of the spin-spin correlation coefficients for almost all realizations of the random couplings. When we sample the whole phase space we find that this distribution is so broad indeed that at low temperatures it essentially becomes uniform, with all possible correlation values appearing with the same probability. The distribution of correlations inside a single phase space valley is also studied and found to be much narrower.Comment: Added a few references and a comment phras

Production of O(1D) following electron impact on CO2

We have studied the excitation of metastable O(1D) following dissociative excitation of CO2 in the electron impact energy range from threshold to 400 eV. A solid Ne matrix at ∼20 K forms the heart of the detector. This is sensitive to the metastable species through the formation of excited excimers (NeO*), The resultant excimer radiation is readily detected, providing a means of measuring the production of the metastables. Using a pulsed electron beam and time-of-flight techniques, we have measured the O(1D) kinetic energy spectrum and its relative production cross sections as a function of electron impact energy. Threshold energy data are used to gain information about the excitation channels involved. In addition, an emission excitation function for the red photons, emitted in coincidence with the exciting electron pulse, has been measured in the 0–400 eV energy range