Contour methods for long-range Ising models: weakening nearest-neighbor interactions and adding decaying fields

We consider ferromagnetic long-range Ising models which display phase transitions. They are long-range one-dimensional Ising ferromagnets, in which the interaction is given by $J_{x,y} = J(|x-y|)\equiv \frac{1}{|x-y|^{2-\alpha}}$ with $\alpha \in [0, 1)$, in particular, $J(1)=1$. For this class of models one way in which one can prove the phase transition is via a kind of Peierls contour argument, using the adaptation of the Fr\"ohlich-Spencer contours for $\alpha \neq 0$, proposed by Cassandro, Ferrari, Merola and Presutti. As proved by Fr\"ohlich and Spencer for $\alpha=0$ and conjectured by Cassandro et al for the region they could treat, $\alpha \in (0,\alpha_{+})$ for $\alpha_+=\log(3)/\log(2)-1$, although in the literature dealing with contour methods for these models it is generally assumed that $J(1)\gg1$, we can show that this condition can be removed in the contour analysis. In addition, combining our theorem with a recent result of Littin and Picco we prove the persistence of the contour proof of the phase transition for any $\alpha \in [0,1)$. Moreover, we show that when we add a magnetic field decaying to zero, given by $h_x= h_*\cdot(1+|x|)^{-\gamma}$ and $\gamma >\max\{1-\alpha, 1-\alpha^* \}$ where $\alpha^*\approx 0.2714$, the transition still persists.Comment: 13 page

Effect of Oscillating Landau Bandwidth on the Integer Quantum Hall Effect in a Unidirectional Lateral Superlattice

We have measured activation gaps for odd-integer quantum Hall states in a unidirectional lateral superlattice (ULSL) -- a two-dimensional electron gas (2DEG) subjected to a unidirectional periodic modulation of the electrostatic potential. By comparing the activation gaps with those simultaneously measured in the adjacent section of the same 2DEG sample without modulation, we find that the gaps are reduced in the ULSL by an amount corresponding to the width acquired by the Landau levels through the introduction of the modulation. The decrement of the activation gap varies with the magnetic field following the variation of the Landau bandwidth due to the commensurability effect. Notably, the decrement vanishes at the flat band conditions.Comment: 7 pages, 6 figures, minor revisio

Tarsometatarsal joint communication during fluoroscopy-guided therapeutic joint injections and relationship with patient age and degree of osteoarthritis.

OBJECTIVE: Although the tarsometatarsal joints are separated into three distinct synovial compartments, communications between adjacent compartments are often noted during image-guided injections. This study aims to determine whether abnormal inter-compartment tarsometatarsal joint communication is associated with patient age or degree of tarsometatarsal osteoarthritis. MATERIALS AND METHODS: One hundred forty tarsometatarsal injections were retrospectively reviewed by two radiologists. Extent of inter-compartment communication and degree of osteoarthritis were independently scored. Univariate and multivariable analyses were performed to assess whether the presence of and number of abnormal joint communications were related to age and degree of osteoarthritis. RESULTS: Forty out of 140 tarsometatarsal joints showed abnormal communication with a separate synovial compartment, and 3 of the 40 showed abnormal communication with two separate compartments. On univariate analysis, higher grade osteoarthritis (p \u3c 0.001) and older age (p = 0.014) were associated with an increased likelihood of abnormal inter-compartment tarsometatarsal communication and a greater number of these abnormal communications. On multivariate analysis, the degree of osteoarthritis remained a significant predictor of the presence of (p \u3c 0.001) and number of (p \u3c 0.001) abnormal communications, while the association of age was not statistically significant. There was significant correlation between age and degree of osteoarthritis (p \u3c 0.001). CONCLUSION: Higher grade osteoarthritis increases the likelihood of abnormal inter-compartment tarsometatarsal joint communication and is associated with a greater number of abnormal communications. Diagnostic injection to localize a symptomatic tarsometatarsal joint may be less reliable in the setting of advanced osteoarthritis

Comparative geochemical evaluation of toxic metals pollution and bacterial communities of industrial effluent tributary and a receiving estuary in Nigeria

Toxic metals/metalloid contaminations of estuarine sediments due to compromised tributaries arouse significant interest in studying bacterial community that triggers natural attenuation processes. Geo-accumulation index (Igeo), contamination factor (CF), pollution load index (PLI), and Hakanson potential ecological risk index (RI) as a sum of risk factors (Er) were used to quantify toxic metal/metalloid-pollution status of Lagos Lagoon (2W) and ‘Iya-Alaro’ tributary (4W) sediments in comparison with pristine ‘Lekki Conservation Centre’ sediment (L1-B). Bacteriology of the ecosystems was based on culture-independent analyses using pyrosequencing. 2W and 4W were extremely contaminated with mercury (Igeo > 7), whereas, cadmium contamination was only observed in 4W. The two ecosystems were polluted with toxic metal based on PLI, where mercury (Er = 2900 and 1900 for 4W and 2W, respectively) posed very high ecological risks. Molecular fingerprinting revealed that Proteobacteria, Firmicutes, and Acidobacteria predominately contributed the 20 most abundant genera in the two ecosystems. The 240 and 310 species present in 2W and 4W, respectively, but absent in L1-B, thrive under the metal concentrations in the polluted hydrosphere. Whereas, the 58,000 species missing in 2W and 4W but found in L1-B would serve as indicators for systems impacted with metal eco-toxicity. Despite toxic metal pollution of the ecosystems understudied, bacterial communities play vital roles in self-recovery processes occurring in the hydrosphere