Metallic ferromagnetism without exchange splitting

In the band theory of ferromagnetism there is a relative shift in the position of majority and minority spin bands due to the self-consistent field due to opposite spin electrons. In the simplest realization, the Stoner model, the majority and minority spin bands are rigidly shifted with respect to each other. Here we consider models at the opposite extreme, where there is no overall shift of the energy bands. Instead, upon spin polarization one of the bands broadens relative to the other. Ferromagnetism is driven by the resulting gain in kinetic energy. A signature of this class of mechanisms is that a transfer of spectral weight in optical absorption from high to low frequencies occurs upon spin polarization. We show that such models arise from generalized tight binding models that include off-diagonal matrix elements of the Coulomb interaction. For certain parameter ranges it is also found that reentrant ferromagnetism occurs. We examine properties of these models at zero and finite temperatures, and discuss their possible relevance to real materials

Estimates of Presumed Population Immunity to SARS-CoV-2 by State in the United States, August 2021

Background: Information is needed to monitor progress toward a level of population immunity to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) sufficient to disrupt viral transmission. We estimated the percentage of the US population with presumed immunity to SARS-CoV-2 due to vaccination, natural infection, or both as of August 26, 2021. Methods: Publicly available data as of August 26, 2021, from the Centers for Disease Control and Prevention were used to calculate presumed population immunity by state. Seroprevalence data were used to estimate the percentage of the population previously infected with SARS-CoV-2, with adjustments for underreporting. Vaccination coverage data for both fully and partially vaccinated persons were used to calculate presumed immunity from vaccination. Finally, we estimated the percentage of the total population in each state with presumed immunity to SARS-CoV-2, with a sensitivity analysis to account for waning immunity, and compared these estimates with a range of population immunity thresholds. Results: In our main analysis, which was the most optimistic scenario, presumed population immunity varied among states (43.1% to 70.6%), with 19 states with ≤60% of their population having been infected or vaccinated. Four states had presumed immunity greater than thresholds estimated to be sufficient to disrupt transmission of less infectious variants (67%), and none were greater than the threshold estimated for more infectious variants (≥78%). Conclusions: The United States remains a distance below the threshold sufficient to disrupt viral transmission, with some states remarkably low. As more infectious variants emerge, it is critical that vaccination efforts intensify across all states and ages for which the vaccines are approved

The Williams Scale of Attitude toward Paganism: development and application among British Pagans

This article builds on the tradition of attitudinal measures of religiosity established by Leslie Francis and colleagues with the Francis Scale of Attitude toward Christianity (and reflected in the Sahin-Francis Scale of Attitude toward Islam, the Katz-Francis Scale of Attitude toward Judaism, and the Santosh-Francis Scale of Attitude toward Hinduism) by introducing a new measure to assess the attitudinal disposition of Pagans. A battery of items was completed by 75 members of a Pagan Summer Camp. These items were reduced to produce a 21-item scale that measured aspects of Paganism concerned with: the God/Goddess, worshipping, prayer, and coven. The scale recorded an alpha coefficient of 0.93. Construct validity of the Williams Scale of Attitude toward Paganism was demonstrated by the clear association with measures of participation in private rituals