Measuring the Decorrelation Times of Fourier Modes in Simulations

We describe a method to study the rate at which modes decorrelate in numerical simulations. We study the XY model updated with the Metropolis and Wolff dynamics respectively and compute the rate at which each eigenvector of the dynamics decorrelates. Our method allows us to identify the decorrelation time for each mode separately. We find that the autocorrelation function of the various modes is markedly different for the `local' Metropolis compared to the `non-local' Wolff dynamics. Equipped with this new insight, it may be possible to devise highly efficient algorithms.Comment: 16 pp (LaTeX), PUPT-1378 , IASSNS-HEP-93/

Halting indigenous biodiversity decline: ambiguity, equity, and outcomes in RMA assessment of significance

In New Zealand, assessment of ‘significance’ is undertaken to give effect to a legal requirement for local authorities to provide for protection of significant sites under the Resource Management Act (1991). The ambiguity of the statute enables different interests to define significance according to their goals: vested interests (developers), local authorities, and non-vested interests in pursuit of protection of environmental public goods may advance different definitions. We examine two sets of criteria used for assessment of significance for biological diversity under the Act. Criteria adapted from the 1980s Protected Natural Areas Programme are inadequate to achieve the maintenance of biological diversity if ranking is used to identify only highest priority sites. Norton and Roper-Lindsay (2004) propose a narrow definition of significance and criteria that identify only a few high-quality sites as significant. Both sets are likely to serve the interests of developers and local authorities, but place the penalty of uncertainty on non-vested interests seeking to maintain biological diversity, and are likely to exacerbate the decline of biological diversity and the loss of landscape-scale processes required for its persistence. When adopting criteria for assessment of significance, we suggest local authorities should consider whose interests are served by different criteria sets, and who will bear the penalty of uncertainty regarding biological diversity outcomes. They should also ask whether significance criteria are adequate, and sufficiently robust to the uncertainty inherent in the assessment of natural values, to halt the decline of indigenous biological diversity

Effective Field Theories

Effective field theories encode the predictions of a quantum field theory at low energy. The effective theory has a fairly low ultraviolet cutoff. As a result, loop corrections are small, at least if the effective action contains a term which is quadratic in the fields, and physical predictions can be read straight from the effective Lagrangean. Methods will be discussed how to compute an effective low energy action from a given fundamental action, either analytically or numerically, or by a combination of both methods. Basically,the idea is to integrate out the high frequency components of fields. This requires the choice of a "blockspin",i.e. the specification of a low frequency field as a function of the fundamental fields. These blockspins will be the fields of the effective field theory. The blockspin need not be a field of the same type as one of the fundamental fields, and it may be composite. Special features of blockspins in nonabelian gauge theories will be discussed in some detail. In analytical work and in multigrid updating schemes one needs interpolation kernels \A from coarse to fine grid in addition to the averaging kernels $C$ which determines the blockspin. A neural net strategy for finding optimal kernels is presented. Numerical methods are applicable to obtain actions of effective theories on lattices of finite volume. The constraint effective potential) is of particular interest. In a Higgs model it yields the free energy, considered as a function of a gauge covariant magnetization. Its shape determines the phase structure of the theory. Its loop expansion with and without gauge fields can be used to determine finite size corrections to numerical data.Comment: 45 pages, 9 figs., preprint DESY 92-070 (figs. 3-9 added in ps format

The Dynamics of a Meandering River

We present a statistical model of a meandering river on an alluvial plane which is motivated by the physical non-linear dynamics of the river channel migration and by describing heterogeneity of the terrain by noise. We study the dynamics analytically and numerically. The motion of the river channel is unstable and we show that by inclusion of the formation of ox-bow lakes, the system may be stabilised. We then calculate the steady state and show that it is in agreement with simulations and measurements of field data.Comment: Revtex, 12 pages, 2 postscript figure

Perturbative Thermodynamics of Lattice QCD with Chiral-Invariant Four-Fermion Interactions

Lattice QCD with additional chiral-invariant four-fermion interactions is studied at nonzero temperature. Staggered Kogut-Susskind quarks are used. The four-fermion interactions are implemented by introducing bosonic auxiliary fields. A mean field treatment of the auxiliary fields is used to calculate the model's asymptotic scale parameter and perturbative thermodynamics, including the one-loop gluonic contributions to the energy, entropy, and pressure. In this approach the calculations reduce to those of ordinary lattice QCD with massive quarks. Hence, the previous calculations of these quantities in lattice QCD using massless quarks are generalized to the massive case.Comment: 22 pages, RevTeX, 8 EPS figures, uses epsf.sty and feynmf.st

Strong coupling expansion of chiral models

A general precedure is outlined for an algorithmic implementation of the strong coupling expansion of lattice chiral models on arbitrary lattices. A symbolic character expansion in terms of connected values of group integrals on skeleton diagrams may be obtained by a fully computerized approach.Comment: 2 pages, PostScript file, contribution to conference LATTICE '9

Lessons from QCD2(N→∞)QCD_2 (N\to\infty): Vacuum structure, Asymptotic Series, Instantons and all that

We discuss two dimensional $QCD (N_c\to\infty)$ with fermions in the fundamental as well as adjoint representation. We find factorial growth $\sim (g^2N_c\pi)^{2k}\frac{(2k)!(-1)^{k-1}}{(2 \pi)^{2k}}$ in the coefficients of the large order perturbative expansion. We argue that this behavior is related to classical solutions of the theory, instantons, thus it has nonperturbative origin. Phenomenologically such a growth is related to highly excited states in the spectrum. We also analyze the heavy-light quark system $Q\bar{q}$ within operator product expansion (which it turns out to be an asymptotic series). Some vacuum condensates \la\bar{q}(x_{\mu}D_{\mu})^{2n}q\ra\sim (x^2)^n\cdot n! which are responsible for this factorial growth are also discussed. We formulate some general puzzles which are not specific for 2D physics, but are inevitable features of any asymptotic expansion. We resolve these apparent puzzles within $QCD_2$ and we speculate that analogous puzzles might occur in real 4-dimensional QCD as well.Comment: latex, 26 pages. A final version to appear in Phys. Rev.

Renormalization group of probabilistic cellular automata with one absorbing state

We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small transition probability one of the cellular automata reduces to the contact process revealing that the cellular automata are in the same universality class as that process, as expected. Better numerical results are obtained as the approximations for the stationary distribution are improved.Comment: Errors in some formulas have been corrected. Additional material available at http://mestre.if.usp.br/~javie

Cluster Algorithm for a Solid-On-Solid Model with Constraints

We adapt the VMR (valleys-to-mountains reflections) algorithm, originally devised by us for simulations of SOS models, to the BCSOS model. It is the first time that a cluster algorithm is used for a model with constraints. The performance of this new algorithm is studied in detail in both phases of the model, including a finite size scaling analysis of the autocorrelations.Comment: 10 pages, 3 figures appended as ps-file

Diffractive Higgs Production by AdS Pomeron Fusion

The double diffractive Higgs production at central rapidity is formulated in terms of the fusion of two AdS gravitons/Pomerons first introduced by Brower, Polchinski, Strassler and Tan in elastic scattering. Here we propose a simple self-consistent holographic framework capable of providing phenomenologically compelling estimates of diffractive cross sections at the LHC. As in the traditional weak coupling approach, we anticipate that several phenomenological parameters must be tested and calibrated through factorization for a self-consistent description of other diffractive process such as total cross sections, deep inelastic scattering and heavy quark production in the central region.Comment: 53 pages, 8 figure