On a microcanonical relation between continuous and discrete spin models

A relation between a class of stationary points of the energy landscape of continuous spin models on a lattice and the configurations of a Ising model defined on the same lattice suggests an approximate expression for the microcanonical density of states. Based on this approximation we conjecture that if a O(n) model with ferromagnetic interactions on a lattice has a phase transition, its critical energy density is equal to that of the n = 1 case, i.e., a system of Ising spins with the same interactions. The conjecture holds true in the case of long-range interactions. For nearest-neighbor interactions, numerical results are consistent with the conjecture for n=2 and n=3 in three dimensions. For n=2 in two dimensions (XY model) the conjecture yields a prediction for the critical energy of the Berezinskij-Kosterlitz-Thouless transition, which would be equal to that of the two-dimensional Ising model. We discuss available numerical data in this respect.Comment: 5 pages, no figure

Kinetic energy and microcanonical nonanalyticities in finite and infinite systems

In contrast to the canonical case, microcanonical thermodynamic functions can show nonanalyticities also for finite systems. In this paper we contribute to the understanding of these nonanalyticities by working out the relation between nonanalyticities of the microcanonical entropy and its configurational counterpart. If the configurational microcanonical entropy $\omega_N^c(v)$ has a nonanalyticity at $v=v_c$, then the microcanonical entropy $\omega_N(\epsilon)$ has a nonanalyticity at the same value $\epsilon=v_c$ of its argument for any finite value of the number of degrees of freedom $N$. The presence of the kinetic energy weakens the nonanalyticities such that, if the configurational entropy is $p$ times differentiable, the entropy is $p+\lfloor N/2 \rfloor$-times differentiable. In the thermodynamic limit, however, the behaviour is very different: The nonanalyticities do not longer occur at the same values of the arguments, but the nonanalyticity of the microcanonical entropy is shifted to a larger energy. These results give a general explanation of the peculiar behaviour previously observed for the mean-field spherical model. With the hypercubic model we provide a further example illustrating our results.Comment: 14 pages, 2 figures; v2: minor corrections, final versio

Numerical elimination and moduli space of vacua

We propose a new computational method to understand the vacuum moduli space of (supersymmetric) field theories. By combining numerical algebraic geometry (NAG) and elimination theory, we develop a powerful, efficient, and parallelizable algorithm toextract important information such as the dimension, branch structure, Hilbert series and subsequent operator counting, as well as variation according to coupling constants and mass parameters. We illustrate this method on a host of examples from gauge theory, string theory, and algebraic geometry

Exploring the energy landscape of <I>XY</I> models

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USCA service utilization in the city of Florence (Italy) during the COVID-19 pandemic

BACKGROUND: In order to support primary care during the first pandemic wave (March 2020), the Italian Government instituted multiprofessional health teams called “USCA” (Special Continuity Care Units), which ensured continuity of care for COVID-19 patients who do not need hospitalization. The aim of our study was to compare the volumes of USCA service utilization in Florence (Tuscany, Italy) during the peak of home visits of three pandemic waves. METHODS: This single-center study followed a retrospective cross-sectional design. The USCA of the Heath District of Florence served a population of 366,190 people. The following data were collected: home medical visits, nursing home (NH) visits, visits in health-care hotels. The peak periods of three epidemic waves were considered in the analyses: the second wave (23 October - 20 November 2020), the third wave (25 March - 22 April 2021), and the Omicron period (27 December 2021 - 6 February 2022). The maximum 7-day moving averages of the daily number of visits during the three periods were calculated. Relative percent differences for visits comparing the considered periods were computed. RESULTS: Home visits during the third pandemic wave increased by 14% compared to the second wave (second wave: N = 1370, third wave: N = 1562), while a decrease was observed during the Omicron period (Omicron vs third wave: -21%; peak value: 41 vs 60). Visits in health-care hotels during the third wave doubled compared to the second wave. After the start of the COVID-19 vaccination campaign, NH visits steeply declined (third wave vs second wave: -95%; N = 323 vs 15; peak value= 14 vs 2 visits per day). During the Omicron period, NH visits increased by almost four times compared to the third wave period. CONCLUSIONS: The USCA service utilization was significant in all the analyzed periods. In a pandemic context, it is necessary to strengthen primary care services such as USCA, which have proved to respond to rapidly changing health needs. KEY MESSAGES: • The USCA service is an innovative model of integrated home care that has proved to respond to rapidly changing health needs during all phases of the COVID-19 pandemic. • The USCA service utilization was significant during all phases of the pandemic. The USCA service has introduced new ways of working and new relationships between services in primary care

Finding all flux vacua in an explicit example

We explicitly construct all supersymmetric flux vacua of a particular Calabi-Yau compactification of type IIB string theory for a small number of flux carrying cycles and a given D3-brane tadpole. The analysis is performed in the large complex structure region by using the polynomial homotopy continuation method, which allows to find all stationary points of the polynomial equations that characterize the supersymmetric vacuum solutions. The number of vacua as a function of the D3 tadpole is in agreement with statistical studies in the literature. We calculate the available tuning of the cosmological constant from fluxes and extrapolate to scenarios with a larger number of flux carrying cycles. We also verify the range of scales for the moduli and gravitino masses recently found for a single explicit flux choice giving a K\"ahler uplifted de Sitter vacuum in the same construction.Comment: LaTeX, 1-32 pages, 8 figure