The sign problem in Monte Carlo simulations of frustrated quantum spin systems

We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and antiferromagnetic couplings $J_{xy}(r)=-J_z(r)$ in the $xy$-plane, for arbitrary distances $r$) the sign problem present for algorithms operating in the $z$-basis can be solved within a recent ``operator-loop'' formulation of the stochastic series expansion method (a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of ${\rm exp}(-\beta H)$ to all orders). The solution relies on identification of operator-loops which change the configuration sign when updated (``merons'') and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models (Phys. Rev. Lett. {\bf 83}, 3116 (1999)). Some important expectation values, e.g., the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.Comment: 13 pages, 16 figure

Quantum Monte Carlo with Directed Loops

We introduce the concept of directed loops in stochastic series expansion and path integral quantum Monte Carlo methods. Using the detailed balance rules for directed loops, we show that it is possible to smoothly connect generally applicable simulation schemes (in which it is necessary to include back-tracking processes in the loop construction) to more restricted loop algorithms that can be constructed only for a limited range of Hamiltonians (where back-tracking can be avoided). The "algorithmic discontinuities" between general and special points (or regions) in parameter space can hence be eliminated. As a specific example, we consider the anisotropic S=1/2 Heisenberg antiferromagnet in an external magnetic field. We show that directed loop simulations are very efficient for the full range of magnetic fields (zero to the saturation point) and anisotropies. In particular for weak fields and anisotropies, the autocorrelations are significantly reduced relative to those of previous approaches. The back-tracking probability vanishes continuously as the isotropic Heisenberg point is approached. For the XY-model, we show that back-tracking can be avoided for all fields extending up to the saturation field. The method is hence particularly efficient in this case. We use directed loop simulations to study the magnetization process in the 2D Heisenberg model at very low temperatures. For LxL lattices with L up to 64, we utilize the step-structure in the magnetization curve to extract gaps between different spin sectors. Finite-size scaling of the gaps gives an accurate estimate of the transverse susceptibility in the thermodynamic limit: chi_perp = 0.0659 +- 0.0002.Comment: v2: Revised and expanded discussion of detailed balance, error in algorithmic phase diagram corrected, to appear in Phys. Rev.

A solution scan of societal options to reduce transmission and spread of respiratory viruses: SARS-CoV-2 as a case study

Societal biosecurity – measures built into everyday society to minimize risks from pests and diseases – is an important aspect of managing epidemics and pandemics. We aimed to identify societal options for reducing the transmission and spread of respiratory viruses. We used SARS-CoV-2 (severe acute respiratory syndrome coronavirus 2) as a case study to meet the immediate need to manage the COVID-19 pandemic and eventually transition to more normal societal conditions, and to catalog options for managing similar pandemics in the future. We used a ‘solution scanning’ approach. We read the literature; consulted psychology, public health, medical, and solution scanning experts; crowd-sourced options using social media; and collated comments on a preprint. Here, we present a list of 519 possible measures to reduce SARS-CoV-2 transmission and spread. We provide a long list of options for policymakers and businesses to consider when designing biosecurity plans to combat SARS-CoV-2 and similar pathogens in the future. We also developed an online application to help with this process. We encourage testing of actions, documentation of outcomes, revisions to the current list, and the addition of further options.</p

Reduced partition function ratios of iron and oxygen in goethite

First-principles calculations based on the density functional theory (DFT) with or without the addition of a Hubbard U correction, are performed on goethite in order to determine the iron and oxygen reduced partition function ratios (β-factors). The calculated iron phonon density of states (pDOS), force constant and β-factor are compared with reevaluated experimental β-factors obtained from Nuclear Resonant Inelastic X-ray Scattering (NRIXS) measurements. The reappraisal of old experimental data is motivated by the erroneous previous interpretation of the low- and high-energy ends of the NRIXS spectrum of goethite and jarosite samples (Dauphas et al., 2012). Here the NRIXS data are analyzed using the SciPhon software that corrects for non-constant baseline. New NRIXS measurements also demonstrate the reproducibility of the results. Unlike for hematite and pyrite, a significant discrepancy remains between DFT, NRIXS and the existing Mössbauer-derived data. Calculations suggest a slight overestimation of the NRIXS signal possibly related to the baseline definition. The intrinsic features of the samples studied by NRIXS and Mössbauer spectroscopy may also contribute to the discrepancy (e.g., internal structural and/or chemical defects, microstructure, surface contribution). As for oxygen, DFT results indicate that goethite and hematite have similar β-factors, which suggests almost no fractionation between the two minerals at equilibrium

Grain size, composition, porosity and permeability contrasts within cross-bedded sandstones in Tertiary fluvial deposits, central Spain

Permeability measured with a portable probe pcrmcflmeter on outcrops of cross·bcdded sandstones ranges betwecn 0·9 and 19 O. The highest pcrmeability (2-19 0 with an avcrage of8·5 D) occurs in thc coarsest grained foresct laminae (CFL). intermediate values (2-120 with an average of 5·3 D) occur in fincr grained foreset laminac (FFL) and thc lowest values (0·9-1 0 0 with un avcrage of 4·8 D) occur in boltomsct laycrs (BL). In the cross·bcds the uverage grain sizc rangcs from medium graincd sand in the CFL to finc grained s,lnd in thc FFL and BL. In all three subf'lcies. the average size of the primary pores is approximately It/> unit smaller than the averagc grain size. The abundance of unstablc carbonatc clasts correlatcs with incrcasing avcrage grain size, micritic clasts being most abundant in the CFL. Converscly. quartz content incrcascs with decreasing grain size and is highest in the FFL and BL. Oiagenetic destruction of primary porosity by compact ion and cementation. as well �IS generation of sccondary porosity through dissolution, were controlled by the original mineralogical composition of the sand. Contrasts in grain size detcrmine the primary pore size contrasts and differences in composition bctwecn CFL. FFL and BL. Permeability contrasts reflect variations in averagc primary pore size rather than differenccs in total porosity. Probe permeability contrasts between eFL. FFL and BL depend on contrasts in llverage pore size and contrasts in mineralogical composition between the subfacies