"Exact" Algorithm for Random-Bond Ising Models in 2D

We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the partition function and correlation functions at a single temperature on any planar network of N Ising spins in O(N^{3/2}) time or less. The method can handle continuous or discrete bond disorder and is especially efficient in the case of bond or site dilution, where it executes in O(L^2 ln L) time near the percolation threshold. We demonstrate its feasibility on the ferromagnetic Ising model and the +/- J random-bond Ising model (RBIM) and discuss the regime of applicability in cases of full frustration such as the Ising antiferromagnet on a triangular lattice.Comment: 4.2 pages, 5 figures, accepted for publication in Phys. Rev. Let

Noise Predictions for STM in Systems with Local Electron Nematic Order

We propose that thermal noise in local stripe orientation should be readily detectable via STM on systems in which local stripe orientations are strongly affected by quenched disorder. Stripes, a unidirectional, nanoscale modulation of electronic charge, are strongly affected by quenched disorder in two-dimensional and quasi-two-dimensional systems. While stripe orientations tend to lock to major lattice directions, dopant disorder locally breaks rotational symmetry. In a host crystal with otherwise $C_4$ rotational symmetry, stripe orientations in the presence of quenched disorder map to the random field Ising model. While the low temperature state of such a system is generally a stripe glass in two dimensional or strongly layered systems, as the temperature is raised, stripe orientational fluctuations become more prevalent. We propose that these thermally excited fluctuations should be readily detectable in scanning tunneling spectroscopy as {\em telegraph noise} in the high voltage part of the local $I(V)$ curves. We predict the spatial, temporal, and thermal evolution of such noise, including the circumstances under which such noise is most likely to be observed. In addition, we propose an in-situ test, amenable to any local scanning probe, for assessing whether such noise is due to correlated fluctuations rather than independent switchers.Comment: 8 pages, 8 figure

Calcium intake, physical activity and bone health status among Chinese early adolescents

The objective of this cross-sectional study was to determine the relationship between calcium intake and physical activity with bone health status among Chinese early adolescents. A selfadministered questionnaire was used to obtain socio-demographic background, family history of osteoporosis, lifestyle practices and eating habits; while daily calcium intake was assessed using one-day dietary recall and two-day dietary record. Physical activity was examined using PAQ-A (Physical Activity Questionnaire for Adolescents). Height, weight and bone health status was assessed using stadiometer, weighing scale (TANITA), and ultrasonometry QUS-2, respectively. Data was analysed using the Statistical Package for Social Sciences (SPSS), version 15.0. A total of 236 Chinese subjects were recruited into this study. The mean age of subjects was 13.6 ± 0.5 years old. Mean daily calcium intake was low, that is 573.4 ± 405.1mg. The mean score of PAQ-A was 2.14 ± 0.64. Mean weight, height, and BMI were 50.9 ± 11.4kg, 1.62 ± 0.08m and 19.40 ± 3.72kg/m2, respectively. Based on CDC classification of BMI-for-age (2000), 68.2% of subjects were in the normal category, 16.1% were underweight, 11.4% were at risk of overweight and 4.2% overweight. Mean Broadband Ultrasound Attenuation (BUA) was 77.55 ± 11.73dB/MHz. According to diagnostic criteria for osteoporosis by WHO (1994), 49.2% of subjects had normal bone mass (t-score > -1.0), more than half of the subjects were either osteopenic (49.6%) or osteopototic (1.3%). This might be due to subjects being in the early adolescents state and their peak bone mass has yet to be attained. T-test showed that there was significant difference between mean body weight among male and female subjects. There was also significant higher mean BUA among female subjects than their counterparts. Pearson correlation test showed that there was no significant relationship between BUA with calcium intake (r= -0.05, p= 0.42) or physical activity (r= 0.03, p= 0.69). However, weight had a significant positive correlation with BUA (r= 0.39, p<0.05). In conclusion, female subjects have better bone health status as compared to males. Although no significant relationship was shown between calcium intake and physical activity with bone health, these two factors are known to reduce future risk of osteoporosis. It is recommended that prevention and management of low bone mass should be focused on factors recognised as determinants of bone health status among early adolescents. This is to ensure optimal bone health being attained among the young population in reducing risk of osteoporosis in future

Mystery of Excess Low Energy States in a Disordered Superconductor in a Zeeman Field

Tunneling density of states measurements of disordered superconducting (SC) Al films in high Zeeman fields reveal a significant population of subgap states which cannot be explained by standard BCS theory. We provide a natural explanation of these excess states in terms of a novel disordered Larkin-Ovchinnikov (dLO) phase that occurs near the spin-paramagnetic transition at the Chandrasekhar-Clogston critical field. The dLO superconductor is characterized by a pairing amplitude that changes sign at domain walls. These domain walls carry magnetization and support Andreev bound states, which lead to distinct spectral signatures at low energy.Comment: 5 pages, 4 figures, plus supplementary section describing methods (2 pages

Bond-Propagation Algorithm for Thermodynamic Functions in General 2D Ising Models

Recently, we developed and implemented the bond propagation algorithm for calculating the partition function and correlation functions of random bond Ising models in two dimensions. The algorithm is the fastest available for calculating these quantities near the percolation threshold. In this paper, we show how to extend the bond propagation algorithm to directly calculate thermodynamic functions by applying the algorithm to derivatives of the partition function, and we derive explicit expressions for this transformation. We also discuss variations of the original bond propagation procedure within the larger context of Y-Delta-Y-reducibility and discuss the relation of this class of algorithm to other algorithms developed for Ising systems. We conclude with a discussion on the outlook for applying similar algorithms to other models.Comment: 12 pages, 10 figures; submitte

Coulomb blockade and quantum tunnelling in the low-conductivity phase of granular metals

We study the effects of Coulomb interaction and inter-grain quantum tunnelling in an array of metallic grains using the phase-functional approach for temperatures $T$ well below the charging energy $E_{c}$ of individual grains yet large compared to the level spacing in the grains. When the inter-grain tunnelling conductance $g\gg1$, the conductivity $\sigma$ in $d$ dimensions decreases logarithmically with temperature ($\sigma/\sigma_{0}\sim1-\frac{1}{2\pi gd}\ln(gE_{c}/T)$), while for $g\to0$, the conductivity shows simple activated behaviour ($\sigma \sim \exp(-E_c/T)$). We show, for bare tunnelling conductance $g \gtrsim 1$, that the parameter $\gamma \equiv g(1-2/(g\pi)\ln(gE_{c}/T))$ determines the competition between charging and tunnelling effects. At low enough temperatures in the regime $1\gtrsim \gamma \gg 1/\sqrt{\beta E_{c}}$, a charge is shared among a finite number $N=\sqrt{(E_{c}/T)/\ln(\pi/2\gamma z)}$ of grains, and we find a soft activation behaviour of the conductivity, $\sigma\sim z^{-1}\exp(-2\sqrt{(E_{c}/T)\ln(\pi/2\gamma z)})$, where $z$ is the effective coordination number of a grain.Comment: 11 pages REVTeX, 3 Figures. Appendix added, replaced with published versio

Dimers on the Triangular Kagome Lattice

We derive exact results for close-packed dimers on the triangular kagome lattice (TKL), formed by inserting triangles into the triangles of the kagome lattice. Because the TKL is a non-bipartite lattice, dimer-dimer correlations are short-ranged, so that the ground state at the Rokhsar-Kivelson (RK) point of the corresponding quantum dimer model on the same lattice is a short-ranged spin liquid. Using the Pfaffian method, we derive an exact form for the free energy, and we find that the entropy is 1/3 ln2 per site, regardless of the weights of the bonds. The occupation probability of every bond is 1/4 in the case of equal weights on every bond. Similar to the case of lattices formed by corner-sharing triangles (such as the kagome and squagome lattices), we find that the dimer-dimer correlation function is identically zero beyond a certain (short) distance. We find in addition that monomers are deconfined on the TKL, indicating that there is a short-ranged spin liquid phase at the RK point. We also find exact results for the ground state energy of the classical Heisenberg model. The ground state can be ferromagnetic, ferrimagnetic, locally coplanar, or locally canted, depending on the couplings. From the dimer model and the classical spin model, we derive upper bounds on the ground state energy of the quantum Heisenberg model on the TKL.Comment: 9 pages, 7 figures, http://www.physics.purdue.edu/~dyao