New Q matrices and their functional equations for the eight vertex model at elliptic roots of unity

The Q matrix invented by Baxter in 1972 to solve the eight vertex model at roots of unity exists for all values of N, the number of sites in the chain, but only for a subset of roots of unity. We show in this paper that a new Q matrix, which has recently been introduced and is non zero only for N even, exists for all roots of unity. In addition we consider the relations between all of the known Q matrices of the eight vertex model and conjecture functional equations for them.Comment: 20 pages, 2 Postscript figure

Study of a new simulation algorithm for dynamical quarks on the APE-100 parallel computer

First results on the autocorrelation behaviour of a recently proposed fermion algorithm by M. L\"uscher are presented and discussed. The occurence of unexpected large autocorrelation times is explained. Possible improvements are discussed.Comment: 3 pages, compressed ps-file (uufiles), Contribution to Lattice 9

The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity η=2mKN\eta = \frac{2m K}{N} for odd N

Following Baxter's method of producing Q_{72}-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter $\eta = \frac{2m K}{N}$ with odd $N$ where Q_{72} does not exist. We use this new Q-operator to study the functional relations in the Fabricius-McCoy comparison between the root-of-unity eight-vertex model and the superintegrable N-state chiral Potts model. By the compatibility of the constructed Q-operator with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we verify the set of functional relations of the root-of-unity eight-vertex model using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation, References added and updated-Journal versio

Dynamic correlations of antiferromagnetic spin-1/2 XXZ chains at arbitrary temperature from complete diagonalization

All eigenstates and eigenvalues are determined for the spin- 1/2 $XXZ$ chain $H = 2J \sum_i ( S_{i}^{x} S_{i + 1}^{x} + S_{i}^{y} S_{i + 1}^{y} + \Delta S_i^z S_{i + 1}^{z})$ for rings with up to N=16 spins, for anisotropies $\Delta=0 , \cos(0.3\pi)$, and 1. The dynamic spin pair correlations $< S_{l+n}^{\mu}(t) S_l^{\mu} > , (\mu=x,z)$, the dynamic structure factors $S^{\mu}(q,\omega)$, and the intermediate structure factors $I^{\mu}(q,t)$ are calculated for arbitrary temperature T. It is found, that for all T, $S^{z}(q,\omega)$ is mainly concentrated on the region $|\omega| < \varepsilon_2(q)$, where $\varepsilon_2(q)$ is the upper boundary of the two-spinon continuum, although excited states corresponding to a much broader frequency spectrum contribute. This is also true for the Haldane-Shastry model and the frustrated Heisenberg model. The intermediate structure factors $I^{\mu}(q,t)$ for $\Delta \neq 0$ show exponential decay for high T and large q. Within the accessible time range, the time-dependent spin correlation functions do not display the long-time signatures of spin diffusion.Comment: 30 pages, REVTEX, 21 figures, to appear in Physical Review

Properties of the String Operator in the Eight-Vertex Model

The construction of creation operators of exact strings in eigenvectors of the eight vertex model at elliptic roots of unity of the crossing parameter which allow the generation of the complete set of degenerate eigenstates is based on the conjecture that the 'naive' string operator vanishes. In this note we present a proof of this conjecture. Furthermore we show that for chains of odd length the string operator is either proportional to the symmetry operator $S$ or vanishes depending on the precise form of the crossing parameter.Comment: 18 pages, typographic errors correcte

A new Q-matrix in the Eight-Vertex Model

We construct a $Q$-matrix for the eight-vertex model at roots of unity for crossing parameter $\eta=2mK/L$ with odd $L$, a case for which the existing constructions do not work. The new $Q$-matrix \Q depends as usual on the spectral parameter and also on a free parameter $t$. For $t=0$ \Q has the standard properties. For $t\neq 0$, however, it does not commute with the operator $S$ and not with itself for different values of the spectral parameter. We show that the six-vertex limit of \Q(v,t=iK'/2) exists.Comment: 10 pages section on quasiperiodicity added, typo corrected, published versio

Modifying (the grammar of) adjuncts : an introduction

One aspect of the progress being made is that the focus of attention has widened. Adverbials, though still the heart of the matter, now form part of a much larger set of constituent types subsumed under the general syntactic label of adjunct; while modifier has become the semantic counterpart on the same level of generality. So one of the readings of Modifying Adjuncts stands for the focus on this intersection. Moreover, recent years have seen a number of studies which attest an increasing interest in adjunct issues. There is an impressive number of monographs, e.g. Alexiadou (1997), Laenzlinger (1998), Cinque (1999), Pittner (1999), Ernst (2002), which, by presenting in-depth analyses of the syntax of adjuncts, have sharpened the debate on syntactic theorizing. Serious attempts to gain a broader view on adjuncts are witnessed by several collections, see Alexiadou and Svenonius (2000), Austin, Engelberg and Rauh (in progress); of particular importance are the contributions to vol. 12.1 of the Italian Journal of Linguistics (2000), a special issue on adverbs, the Introductions to which by Corver and Delfitto (2000) and Delfitto (2000) may be seen as the best state-of-the-art article on adverbs and adverbial modification currently on the market. To try and test a fresh view on adjuncts was the leitmotif of the Oslo Conference “Approaching the Grammar of Adjuncts” (Sept 22–25, 1999), which provided the initial forum for the papers contained in this volume and initiated a period of discussion and continuing interaction among the contributors, from which the versions published here have greatly profited. The aim of the Oslo conference, and hence the focus of the present volume, was to encourage syntacticians and semanticists to open their minds to a more integrative approach to adjuncts, thereby paying attention to, and attempting to account for, the various interfaces that the grammar of adjuncts crucially embodies. From this perspective, the present volume is to be conceived of as an interim balance of current trends in modifying the views on adjuncts. In introducing the papers, we will refrain from rephrasing the abstracts, but will instead offer a guided tour through the major problem areas they are tackling. Assessed by thematic convergence and mutual reference, the contributions form four groups, which led us to arrange them into subparts of the book. Our commenting on these is intended (i) to provide a first glance at the contents, (ii) to reveal some of the reasons why adjuncts indeed are, and certainly will remain, a challenging issue, and thereby (iii) to show some facets of what we consider novel and promising approaches

Double stars and astrometric uncertainties in Gaia DR1

A significant number of double stars with separations up to 2.5 arcsec are present in the Gaia Data Release 1 astrometric catalogs. Limiting our analysis to a well-studied sample of 1124 doubles resolved by Hipparcos, provided with individual Tycho component photometry, and cross-matched with the TGAS catalog, we estimate a rate of at least 3% for brighter double stars in Gaia DR1, which should be resolved in the future data releases. Gaia astrometric results are affected by unresolved duplicity. The variance-normalized quadratic differences of proper motion between Gaia and Hipparcos do not follow the expected chi^2 distribution and show signs of powerful degradation in the components aligned with the axes of the double systems. This concerns only pairs with separation below 1.2 -- 1.5 arcsec, which mostly remain unresolved in Gaia DR1. On the other hand, the orthogonal proper motion components and parallaxes do not have any detectable perturbation, as well as all astrometry for separations above 1.5 arcsec. Gaia parallaxes do not seem to be perturbed by duplicity, with Gaia - Hipparcos differences being systematically smaller than the expectation. The rate of incorrectly identified, or swapped, companions is estimated at 0.4%.Comment: Accepted in ApJLetter