Error estimation and reduction with cross correlations

Besides the well-known effect of autocorrelations in time series of Monte Carlo simulation data resulting from the underlying Markov process, using the same data pool for computing various estimates entails additional cross correlations. This effect, if not properly taken into account, leads to systematically wrong error estimates for combined quantities. Using a straightforward recipe of data analysis employing the jackknife or similar resampling techniques, such problems can be avoided. In addition, a covariance analysis allows for the formulation of optimal estimators with often significantly reduced variance as compared to more conventional averages.Comment: 16 pages, RevTEX4, 4 figures, 6 tables, published versio

Cross-correlations in scaling analyses of phase transitions

Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced statistical fluctuations at almost no extra cost in terms of computation time.Comment: 4 pages, RevTEX4, 3 tables, 1 figur

A Physiological Assessment of Wetland Habitats for Spring-migrating Ducks in the Agricultural Landscapes of the Southern Prairie Pothole Region

The conversion of grassland and wetland ecosystems in the Prairie Pothole Region (PPR) has been a pervasive challenge for conservationists dating back to the early 1900s. The legacy of ever-increasing agricultural intensity in the southern portions of the PPR, including eastern South Dakota, has left many wetland ecosystems in a matrix of intensive agricultural production. With little surrounding nesting cover, these wetlands are thought to have limited potential for waterfowl reproduction but may still play an important role facilitating migration of waterfowl en route to northern breeding areas during spring. My research sought to understand the contributions of wetlands in intensively-farmed landscapes for spring-migrating ducks. I measured a number of biotic attributes of wetlands including the density of aquatic invertebrates and submersed macrophytes and abundance of spring-migrating ducks. I also measured concentrations of lipid metabolites circulating in plasma of female lesser scaup (Aythya affinis) and bluewinged teal (Anas discors) to understand refueling performance of migrants using wetlands with variable biotic and abiotic characteristics. Duck abundance, refueling performance, and prey abundance were generally similar across the upland cultivation gradient, if not slightly greater in more intensely-farmed landscapes. These results suggested wetlands in intensively-farmed landscapes in eastern South Dakota currently confer similar benefits to migrating waterfowl as those in less intensively-farmed landscapes. An analysis on wetland covariates and migrant refueling performance revealed density of fathead minnows (Pimephales promelas) in wetlands was negatively associated with refueling performance. Further analyses suggested this finding was likely the result of trophic effects of fathead minnows on invertebrate and plant communities in the wetlands. Taken together, my results suggested wetlands in agricultural landscapes in eastern South Dakota can provide novel refueling habitats for migrating ducks when factors such as artificial connectivity or water permanency that facilitate fathead minnow colonization and persistence are controlled. Further, they raise questions about whether wetlands in intensively-farmed landscapes are indeed resilient to adjacent land use or simply compensate for degradation through increased productivity characteristic of landscapes with intensive crop production. Answering this latter question is key for understanding agricultural impacts and setting wetland restoration priorities in the region

Monte Carlo study of the evaporation/condensation transition on different Ising lattices

In 2002 Biskup et al. [Europhys. Lett. 60, 21 (2002)] sketched a rigorous proof for the behavior of the 2D Ising lattice gas, at a finite volume and a fixed excess \delta M of particles (spins) above the ambient gas density (spontaneous magnetisation). By identifying a dimensionless parameter \Delta (\delta M) and a universal constant \Delta_c, they showed in the limit of large system sizes that for \Delta < \Delta_c the excess is absorbed in the background (``evaporated'' system), while for \Delta > \Delta_c a droplet of the dense phase occurs (``condensed'' system). To check the applicability of the analytical results to much smaller, practically accessible system sizes, we performed several Monte Carlo simulations for the 2D Ising model with nearest-neighbour couplings on a square lattice at fixed magnetisation M. Thereby, we measured the largest minority droplet, corresponding to the condensed phase, at various system sizes (L=40, >..., 640). With analytic values for for the spontaneous magnetisation m_0, the susceptibility \chi and the Wulff interfacial free energy density \tau_W for the infinite system, we were able to determine \lambda numerically in very good agreement with the theoretical prediction. Furthermore, we did simulations for the spin-1/2 Ising model on a triangular lattice and with next-nearest-neighbour couplings on a square lattice. Again, finding a very good agreement with the analytic formula, we demonstrate the universal aspects of the theory with respect to the underlying lattice. For the case of the next-nearest-neighbour model, where \tau_W is unknown analytically, we present different methods to obtain it numerically by fitting to the distribution of the magnetisation density P(m).Comment: 14 pages, 17 figures, 1 tabl

2D Potts Model Correlation Lengths: Numerical Evidence for ξo=ξd\xi_o = \xi_d at βt\beta_t

We have studied spin-spin correlation functions in the ordered phase of the two-dimensional $q$-state Potts model with $q=10$, 15, and 20 at the first-order transition point $\beta_t$. Through extensive Monte Carlo simulations we obtain strong numerical evidence that the correlation length in the ordered phase agrees with the exactly known and recently numerically confirmed correlation length in the disordered phase: $\xi_o(\beta_t) = \xi_d(\beta_t)$. As a byproduct we find the energy moments in the ordered phase at $\beta_t$ in very good agreement with a recent large $q$-expansion.Comment: 11 pages, PostScript. To appear in Europhys. Lett. (September 1995). See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional ϕ4\phi^4-Model: Autocorrelations and Interface Tension

We discuss the recently proposed multicanonical multigrid Monte Carlo method and apply it to the scalar $\phi^4$-model on a square lattice. To investigate the performance of the new algorithm at the field-driven first-order phase transitions between the two ordered phases we carefully analyze the autocorrelations of the Monte Carlo process. Compared with standard multicanonical simulations a real-time improvement of about one order of magnitude is established. The interface tension between the two ordered phases is extracted from high-statistics histograms of the magnetization applying histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as uuencoded compressed tar fil

Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths

We report numerical simulations of two-dimensional $q$-state Potts models with emphasis on a new quantity for the computation of spatial correlation lengths. This quantity is the cluster-diameter distribution function $G_{diam}(x)$, which measures the distribution of the diameter of stochastically defined cluster. Theoretically it is predicted to fall off exponentially for large diameter $x$, $G_{diam} \propto \exp(-x/\xi)$, where $\xi$ is the correlation length as usually defined through the large-distance behavior of two-point correlation functions. The results of our extensive Monte Carlo study in the disordered phase of the models with $q=10$, 15, and $20$ on large square lattices of size $300 \times 300$, $120 \times 120$, and $80 \times 80$, respectively, clearly confirm the theoretically predicted behavior. Moreover, using this observable we are able to verify an exact formula for the correlation length $\xi_d(\beta_t)$ in the disordered phase at the first-order transition point $\beta_t$ with an accuracy of about $1$ for all considered values of $q$. This is a considerable improvement over estimates derived from the large-distance behavior of standard (projected) two-point correlation functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm

Finite size scaling analysis of compact QED

We describe results of a high-statistics finite size scaling analysis of 4d compact U(1) lattice gauge theory with Wilson action at the phase transition point. Using a multicanonical hybrid Monte Carlo algorithm we generate data samples with more than 150 tunneling events between the metastable states of the system, on lattice sizes up to 18^4. We performed a first analysis within the Borgs-Kotecky finite size scaling scheme. As a result, we report evidence for a first-order phase transition with a plaquette energy gap, G=0.02667(20), at a transition coupling, beta_T=1.011128(11).Comment: Lattice 2000 (Topics in Gauge Theories),6 pages, 6 figures, LaTe

Temporal Variability in Survival of Non-Breeding Northern Bobwhites in Ohio

Non-breeding season survival is an important determinant of population growth rates of northern bobwhites (Colinus virginianus) and is primarily influenced by hunter harvest, predation, and weather. The collective influence of these factors varies within and among years and across the bobwhite range. Understanding factors that influence variation in survival is important to inform regionally-specific management strategies for declining bobwhite populations. We radiomarked 311 bobwhites from 73 coveys to investigate temporal variation in non-breeding season (Oct-Mar) survival of a declining bobwhite population on private land in southwestern Ohio during 2008–2011. We used the data bootstrapping feature in Program MARK to adjust for overdispersion caused by dependency of survival among members of the same covey. Temporal variation in survival was best modeled (wi 1⁄4 0.935) with weekly differences in survival rates that varied within and between years. There was only slight dependency in survival due to covey affiliation between the 2 seasons (median cˆ 1⁄4 1.51). Non-breeding season survival was low (Sˆ 2009–2010 1⁄4 0.05, 95% CI 1⁄4 0.03-0.11, Sˆ 2010–2011 1⁄4 0.12, 95% CI 1⁄4 0.07- 0.20) in 2 years with data for the entire season. Survival during 10 December-31 March varied among the 3 years (Sˆ2008–2009 1⁄4 0.45, 95% CI 1⁄4 0.29-0.61, Sˆ2009–2010 1⁄4 0.11, 95% CI 1⁄4 0.05-0.21, Sˆ2010–2011 1⁄4 0.25, 95% CI 1⁄4 0.17-0.34). There were 2 periods of low survival; a short period in early fall that coincided with senescence of herbaceous vegetation and the hunting season, and during periods with prolonged snow cover during winter. Late winter survival during periods of snow cover was most variable and winter severity appeared to have the greatest influence on seasonal survival during our study. Management strategies to improve non-breeding season survival in northern populations should focus on managing winter habitat to improve survival during periods of prolonged snow cover

Universal finite-size scaling function for coarsening in the Potts model with conserved dynamics

We study kinetics of phase segregation in multicomponent mixtures via Monte Carlo simulations of the q-state Potts model, in two spatial dimensions, for 2 ≤ q ≤ 20. The associated growth of domains in finite boxes, irrespective of q and temperature, can be described by a single universal finite-size scaling function, with only the introduction of a nonuniversal metric factor in the scaling variable. Our results show that although the scaling function is independent of the type of transition, the q-dependence of the metric factor hints to a crossover at q = 5 where the type of transition in the model changes from second to first order