Ground-water resources of Collier County, Florida

The Biscayne Aquifer is the principal source of water for the heavily populated area in the vicinity of West Palm Beach and Miami. The publication of this data is timely and will assist in the intelligent development of the water resources of the area.The report recognizes two major aquifers as the source of ground water in Collier County. The lower aquifer is highly mineralized, but contains usable water, and the more shallow aquifer is the source of large supplies, which are utilized by municipalities and domestic users. Adequate supplies of fresh water are present in the Naples area and by proper planning, these can be developed in an orderly manner and salt water encroachment can be prevented. (PDF has 99 pages

Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain

We study numerically the paramagnetic phase of the spin-1/2 random transverse-field Ising chain, using a mapping to non-interacting fermions. We extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and to dynamical properties. Our results are consistent with the idea that there are ``Griffiths-McCoy'' singularities in the paramagnetic phase described by a continuously varying exponent $z(\delta)$, where $\delta$ measures the deviation from criticality. There are some discrepancies between the values of $z(\delta)$ obtained from different quantities, but this may be due to corrections to scaling. The average on-site time dependent correlation function decays with a power law in the paramagnetic phase, namely $\tau^{-1/z(\delta)}$, where $\tau$ is imaginary time. However, the typical value decays with a stretched exponential behavior, $\exp(-c\tau^{1/\mu})$, where $\mu$ may be related to $z(\delta)$. We also obtain results for the full probability distribution of time dependent correlation functions at different points in the paramagnetic phase.Comment: 10 pages, 14 postscript files included. The discussion of the typical time dependent correlation function has been greatly expanded. Other papers of APY are available on-line at http://schubert.ucsc.edu/pete

Impurity spin relaxation in S=1/2 XX chains

Dynamic autocorrelations $$ (\alpha=x,z) of an isolated impurity spin in a S=1/2 XX chain are calculated. The impurity spin, defined by a local change in the nearest-neighbor coupling, is either in the bulk or at the boundary of the open-ended chain. The exact numerical calculation of the correlations employs the Jordan-Wigner mapping from spin operators to Fermi operators; effects of finite system size can be eliminated. Two distinct temperature regimes are observed in the long-time asymptotic behavior. At T=0 only power laws are present. At high T the x correlation decays exponentially (except at short times) while the z correlation still shows an asymptotic power law (different from the one at T=0) after an intermediate exponential phase. The boundary impurity correlations follow power laws at all T. The power laws for the z correlation and the boundary correlations can be deduced from the impurity-induced changes in the properties of the Jordan-Wigner fermion states.Comment: Final version to be published in Phys. Rev. B. Three references added, extended discussion of relation to previous wor

Ising Dynamics with Damping

We show for the Ising model that is possible construct a discrete time stochastic model analogous to the Langevin equation that incorporates an arbitrary amount of damping. It is shown to give the correct equilibrium statistics and is then used to investigate nonequilibrium phenomena, in particular, magnetic avalanches. The value of damping can greatly alter the shape of hysteresis loops, and for small damping and high disorder, the morphology of large avalanches can be drastically effected. Small damping also alters the size distribution of avalanches at criticality.Comment: 8 pages, 8 figures, 2 colum

Functional Forms for the Squeeze and the Time-Displacement Operators

Using Baker-Campbell-Hausdorff relations, the squeeze and harmonic-oscillator time-displacement operators are given in the form $\exp[\delta I] \exp[\alpha (x^2)]\exp[\beta(x\partial)] \exp[\gamma (\partial)^2]$, where $\alpha$, $\beta$, $\gamma$, and $\delta$ are explicitly determined. Applications are discussed.Comment: 10 pages, LaTe

An Evaluation Framework for Personalization Strategy Experiment Designs

Online Controlled Experiments (OCEs) are the gold standard in evaluating the effectiveness of changes to websites. An important type of OCE evaluates different personalization strategies, which present challenges in low test power and lack of full control in group assignment. We argue that getting the right experiment setup -- the allocation of users to treatment/analysis groups -- should take precedence of post-hoc variance reduction techniques in order to enable the scaling of the number of experiments. We present an evaluation framework that, along with a few simple rule of thumbs, allow experimenters to quickly compare which experiment setup will lead to the highest probability of detecting a treatment effect under their particular circumstance.Comment: Presented in the AdKDD 2020 workshop, in conjunction with The 26th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2020. Main paper: 7 pages, 2 figures, 2 tables, Supplementary document: 6 page

Critical Behavior and Griffiths-McCoy Singularities in the Two-Dimensional Random Quantum Ising Ferromagnet

We study the quantum phase transition in the two-dimensional random Ising model in a transverse field by Monte Carlo simulations. We find results similar to those known analytically in one-dimension. At the critical point, the dynamical exponent is infinite and the typical correlation function decays with a stretched exponential dependence on distance. Away from the critical point there are Griffiths-McCoy singularities, characterized by a single, continuously varying exponent, z', which diverges at the critical point, as in one-dimension. Consequently, the zero temperature susceptibility diverges for a RANGE of parameters about the transition.Comment: 4 pages RevTeX, 3 eps-figures include

Zero--Temperature Quantum Phase Transition of a Two--Dimensional Ising Spin--Glass

We study the quantum transition at $T=0$ in the spin-$\frac12$ Ising spin--glass in a transverse field in two dimensions. The world line path integral representation of this model corresponds to an effective classical system in (2+1) dimensions, which we study by Monte Carlo simulations. Values of the critical exponents are estimated by a finite-size scaling analysis. We find that the dynamical exponent, $z$, and the correlation length exponent, $\nu$, are given by $z = 1.5 \pm 0.05$ and $\nu = 1.0 \pm 0.1$. Both the linear and non-linear susceptibility are found to diverge at the critical point.Comment: RevTeX 10 pages + 4 figures (appended as uuencoded, compressed tar-file), THP21-9

Correlation functions for the three state superintegrable chiral Potts spin chain of finite lengths

We compute the correlation functions of the three state superintegrable chiral Potts spin chain for chains of length 3,4,5. From these results we present conjectures for the form of the nearest neighbor correlation function.Comment: 10 pages; references update