Ground state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S=1/2 XY model

We present high-precision quantum Monte Carlo results for the S=1/2 XY model on a two-dimensional square lattice, in the ground state as well as at finite temperature. The energy, the spin stiffness, the magnetization, and the susceptibility are calculated and extrapolated to the thermodynamic limit. For the ground state, we test a variety of finite-size scaling predictions of effective Lagrangian theory and find good agreement and consistency between the finite-size corrections for different quantities. The low-temperature behavior of the susceptibility and the internal energy is also in good agreement with theoretical predictions.Comment: 6 pages, 8 figure

Sitting Time, Physical Activity, and Risk of Mortality in Adults

BACKGROUND It is unclear what level of moderate to vigorous intensity physical activity (MVPA) offsets the health risks of sitting. OBJECTIVES The purpose of this study was to examine the joint and stratified associations of sitting and MVPA with all-cause and cardiovascular disease (CVD) mortality, and to estimate the theoretical effect of replacing sitting time with physical activity, standing, and sleep. METHODS A longitudinal analysis of the 45 and Up Study calculated the multivariable-adjusted hazard ratios (HRs) of sitting for each sitting-MVPA combination group and within MVPA strata. Isotemporal substitution modeling estimated the per-hour HR effects of replacing sitting. RESULTS A total of 8,689 deaths (1,644 due to CVD) occurred among 149,077 participants over an 8.9-year (median) follow-up. There was a statistically significant interaction between sitting and MVPA only for all-cause mortality. Sitting time was associated with both mortality outcomes in a nearly dose-response manner in the least active groups reporting <150 MVPA min/week. For example, among those reporting no MVPA, the all-cause mortality HR comparing the most sedentary (>8 h/day) to the least sedentary (<4 h/day) groups was 1.52 (95% confidence interval: 1.13 to 2.03). There was inconsistent and weak evidence for elevated CVD and all-cause mortality risks with more sitting among those meeting the lower (150 to 299 MVPA min/week) or upper ($300 MVPA min/week) limits of the MVPA recommendation. Replacing sitting with walking and MVPA showed stronger associations among high sitters (>6 sitting h/day) where, for example, the per-hour CVD mortality HR for sitting replaced with vigorous activity was 0.36 (95% confidence interval: 0.17 to 0.74). CONCLUSIONS Sitting is associated with all-cause and CVD mortality risk among the least physically active adults; moderate-to-vigorous physical activity doses equivalent to meeting the current recommendations attenuate or effectively eliminate such association

Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model

The low energy behaviour of the 2d antiferromagnetic Heisenberg model is studied in the sector with total spins $S=0,1,2$ by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix $\Delta_S^{(n+1)}$ of 4 neighbouring "$n$ clusters" of size $2^n\times 2^n$, $n=1,2,3,...$ from the corresponding quantities $\Delta_S^{(n)}$. Conservation of total spin $S$ is implemented explicitly and plays an important role. It is shown, how the ground state energies $E_S^{(n+1)}$, $S=0,1,2$ approach each other for increasing $n$, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions $$ between the ground states $|S,m;n+1>$ ($m=-S,...,S$) on an $(n+1)$-cluster of size $2^{n+1}\times 2^{n+1}$, mediated by the staggered spin operator $S_q^*$Comment: 18 pages, 8 figures, RevTe

On the Application of the Non Linear Sigma Model to Spin Chains and Spin Ladders

We review the non linear sigma model approach (NLSM) to spin chains and spin ladders, presenting new results. The generalization of the Haldane's map to ladders in the Hamiltonian approach, give rise to different values of the $\theta$ parameter depending on the spin S, the number of legs $n_{\ell}$ and the choice of blocks needed to built up the NLSM fields. For rectangular blocks we obtain $\theta = 0$ or $2 \pi S$ depending on wether $n_{\ell}$, is even or odd, while for diagonal blocks we obtain $\theta = 2 \pi S n_{\ell}$. Both results agree modulo $2 \pi$, and yield the same prediction, namely that even ( resp. odd) ladders are gapped (resp. gapless). For even legged ladders we show that the spin gap collapses exponentially with $n_{\ell}$ and we propose a finite size correction to the gap formula recently derived by Chakravarty using the 2+1 NSLM, which gives a good fit of numerical results. We show the existence of a Haldane phase in the two legged ladder using diagonal blocks and finally we consider the phase diagram of dimerized ladders.Comment: 25 pages, Latex, 7 figures in postscript files, Proc. of the 1996 El Escorial Summer School on "Strongly Correlated Magnetic and Superconducting Systems". Some more references are adde

Stochastic series expansion method with operator-loop update

A cluster update (the ``operator-loop'') is developed within the framework of a numerically exact quantum Monte Carlo method based on the power series expansion of exp(-BH) (stochastic series expansion). The method is generally applicable to a wide class of lattice Hamiltonians for which the expansion is positive definite. For some important models the operator-loop algorithm is more efficient than loop updates previously developed for ``worldline'' simulations. The method is here tested on a two-dimensional anisotropic Heisenberg antiferromagnet in a magnetic field.Comment: 5 pages, 4 figure

Dynamic Critical Behavior of a Swendsen-Wang-Type Algorithm for the Ashkin-Teller Model

We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin--Teller model. We find that the Li--Sokal bound on the autocorrelation time ($\tau_{{\rm int},{\cal E}} \ge {\rm const} \times C_H$) holds along the self-dual curve of the symmetric Ashkin--Teller model, and is almost but not quite sharp. The ratio $\tau_{{\rm int},{\cal E}} / C_H$ appears to tend to infinity either as a logarithm or as a small power ($0.05 \leq p \leq 0.12$). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.Comment: 59 pages including 3 figures, uuencoded g-compressed ps file. Postscript size = 799740 byte

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The results are seen to match extremely well long large-time asymptotic expansions newly derived here. For our initial conditions we use new long asymptotic expansions for the equal-time pair correlation functions of the transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising model. Using this one can also study the equal-time wavevector-dependent correlation function of the quantum chain, a.k.a. the q-dependent diagonal susceptibility in the 2d Ising model, in great detail with very little computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references added and minor changes of style. vs3: Corrections made and reference adde

Charcoal does not change the decomposition rate of mixed litters in a mineral cambisol: a controlled conditions study

It has been recently shown that the presence of charcoal might promote humus decomposition in the soil. We investigated the decomposition rate of charcoal and litters of different biochemical quality mixed together in a soil incubation under controlled conditions. Despite the large range of organic substrate quality used in this study, we did not find any difference in the decomposition between the average of two individual substrates decomposing separately and the same substrates mixed together. We concluded that charcoal does not always promote other organic matter decomposition and that its particular effect might depend on various factors, for example, soil properties