Anomalously elastic intermediate phase in randomly layered superfluids, superconductors, and planar magnets.

We show that layered quenched randomness in planar magnets leads to an unusual intermediate phase between the conventional ferromagnetic low-temperature and paramagnetic high-temperature phases. In this intermediate phase, which is part of the Griffiths region, the spin-wave stiffness perpendicular to the random layers displays anomalous scaling behavior, with a continuously variable anomalous exponent, while the magnetization and the stiffness parallel to the layers both remain finite. Analogous results hold for superfluids and superconductors. We study the two phase transitions into the anomalous elastic phase, and we discuss the universality of these results, and implications of finite sample size as well as possible experiments.

Demographic, jurisdictional, and spatial effects on social distancing in the United States during the COVID-19 pandemic.

Social distancing, a non-pharmaceutical tactic aimed at reducing the spread of COVID-19, can arise because individuals voluntarily distance from others to avoid contracting the disease. Alternatively, it can arise because of jurisdictional restrictions imposed by local authorities. We run reduced form models of social distancing as a function of county-level exogenous demographic variables and jurisdictional fixed effects for 49 states to assess the relative contributions of demographic and jurisdictional effects in explaining social distancing behavior. To allow for possible spatial aspects of a contagious disease, we also model the spillovers associated with demographic variables in surrounding counties as well as allow for disturbances that depend upon those in surrounding counties. We run our models weekly and examine the evolution of the estimated coefficients over time since the onset of the COVID-19 pandemic in the United States. These estimated coefficients express the revealed preferences of individuals who were able to and chose to stay at home to avoid the disease. Stay-at-home behavior measured using cell phone tracking data exhibits considerable cross-sectional variation, increasing over nine-fold from the end of January 2020 to the end of March 2020, and then decreasing by about 50% through mid-June 2020. Our estimation results show that demographic exogenous variables explain substantially more of this variation than predictions from jurisdictional fixed effects. Moreover, the explanations from demographic exogenous variables and jurisdictional fixed effects show an evolving correlation over the sample period, initially partially offsetting, and eventually reinforcing each other. Furthermore, the predicted social distance from demographic exogenous variables shows substantial spatial autoregressive dependence, indicating clustering in social distancing behavior. The increased variance of stay-at-home behavior coupled with the high level of spatial dependence can result in relatively intense hotspots and coldspots of social distance, which has implications for disease spread and mitigation.

Influence of super-ohmic dissipation on a disordered quantum critical point.

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.