Spin-one bosons in low dimensional Mott insulating states

We analyze the strong coupling limit of spin-one bosons in low dimensional Mott insulating states. In 1D lattices, for an odd number of bosons per site ($N_0$), the ground state is a dimerized valence bond crystal state with a two-fold degeneracy; the low lying elementary spin excitations carry spin one. For an even number of bosons per site, the ground state is a nondegenerate spin singlet Mott state. We also argue that in a square lattice in a quantum disordered limit the ground states should be dimerized valence bond crystals for an odd integer $N_0$. Finally, we briefly report results for non-integer numbers of bosons per site in one-dimensional lattices.Comment: 5 pages; discussions on non-integer case have been shortene

Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems

We demonstrate through two case studies, one on the p-spin interaction model and the other on the random K-satisfiability problem, that a heterogeneity transition occurs to the ground-state configuration space of a random finite-connectivity spin glass system at certain critical value of the constraint density. At the transition point, exponentially many configuration communities emerge from the ground-state configuration space, making the entropy density s(q) of configuration-pairs a non-concave function of configuration-pair overlap q. Each configuration community is a collection of relatively similar configurations and it forms a stable thermodynamic phase in the presence of a suitable external field. We calculate s(q) by the replica-symmetric and the first-step replica-symmetry-broken cavity methods, and show by simulations that the configuration space heterogeneity leads to dynamical heterogeneity of particle diffusion processes because of the entropic trapping effect of configuration communities. This work clarifies the fine structure of the ground-state configuration space of random spin glass models, it also sheds light on the glassy behavior of hard-sphere colloidal systems at relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic

Detection of weak-order phase transitions in ferromagnets by ac resistometry

It is shown that ac resistometry can serve as an effective tool for the detection of phase transitions, such as spin reorientation or premartensitic phase transitions, which generally are not disclosed by dc resistivity measurement. Measurement of temperature dependence of impedance, $Z(T)$, allows one to unmask the anomaly, corresponding to a weak-order phase transition. The appearance of such an anomaly is accounted for by a change in the effective permeability $\mu$ of a sample upon the phase transition. Moreover, frequency dependence of $\mu$ makes it possible to use the frequency of the applied ac current as an adjusting parameter in order to make this anomaly more pronounced. The applicability of this method is tested for the rare earth Gd and Heusler alloy Ni$_2$MnGa.Comment: 4 pages, 2 figures, to be published in J. Appl. Phys., v.94(5

Learning Rich Geographical Representations: Predicting Colorectal Cancer Survival in the State of Iowa

Neural networks are capable of learning rich, nonlinear feature representations shown to be beneficial in many predictive tasks. In this work, we use these models to explore the use of geographical features in predicting colorectal cancer survival curves for patients in the state of Iowa, spanning the years 1989 to 2012. Specifically, we compare model performance using a newly defined metric -- area between the curves (ABC) -- to assess (a) whether survival curves can be reasonably predicted for colorectal cancer patients in the state of Iowa, (b) whether geographical features improve predictive performance, and (c) whether a simple binary representation or richer, spectral clustering-based representation perform better. Our findings suggest that survival curves can be reasonably estimated on average, with predictive performance deviating at the five-year survival mark. We also find that geographical features improve predictive performance, and that the best performance is obtained using richer, spectral analysis-elicited features.Comment: 8 page