Gribov Copies in the Minimal Landau Gauge: the Influence on Gluon and Ghost Propagators

We study the influence of Gribov copies on gluon and ghost propagators, evaluated numerically in pure SU(2) lattice gauge theory in the minimal Landau gauge. Simulations are done at four different values of $\beta$ (namely $\beta$ = 0, 0.8, 1.6 and 2.7) and for volumes up to $16^4$ (up to $24^4$ at $\beta$ = 1.6). For the gluon propagator, Gribov noise seems to be of the order of magnitude of the numerical accuracy, even at very small values of the coupling $\beta$. On the contrary, for the ghost propagator, Gribov noise is clearly observable for the three values of $\beta$ in the strong-coupling regime. In particular, data corresponding to the minimal Landau gauge are always smaller than those obtained in a generic Landau gauge. This result can be qualitatively explained.Comment: 19 pages, including three figures; minor modifications following referee's suggestions. ZiF-MS-16/97 preprint. To appear in Nucl.Phys.

Ancestral processes with selection: Branching and Moran models

We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyze the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced back into the past. The second approach is the Moran model with selection. Here, the population has constant size N. Individuals reproduce (at rates depending on their types), the offspring inherits the parent's type, and replaces a randomly chosen individual (to keep population size constant). Independently of the reproduction process, individuals can change type. As in the branching model, we consider the ancestral lines of single individuals chosen from the equilibrium population. We use analytical results of Fearnhead (2002) to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution in forward time.Comment: minor changes, updated references; Banach Center Publications, in pres

Reassessing Referential Indeterminacy

Quine and Davidson employ proxy functions to demonstrate that the use of language (behaviouristically conceived) is compatible with indefinitely many radically different reference relations. They also believe that the use of language (behaviouristically conceived) is all that determines reference. From this they infer that reference is indeterminate, i.e. that there are no facts of the matter as to what singular terms designate and what predicates apply to. Yet referential indeterminacy yields rather dire consequences. One thus does wonder whether one can hold on to a Quine-Davidson stance in semantics-cum-metaphysics and still avoid embracing referential indeterminacy. I argue that one can. Anyone adhering to the behaviouristic account pivotal to the Quine-Davidson stance is bound to acknowledge certain facts about verbal behaviour – that some utterances are tied to situations, that some utterances are tied to segments in situations, that some predicates have non-contextualised conditions of application, and that use involves causal dependencies. The restrictions from these facts ensure that only reference relations generated by means of rather exceptional proxy functions are compatible with verbal behaviour. I conclude that this allows one to rebuff the Quine-Davidson argument for the indeterminacy of reference, as it were, from within. I moreover tentatively conclude that the line of thought laid out provides good reason for just about anyone to hold that there are facts about reference after all

Critical behaviour and Scaling functions for the three-dimensional O(6) spin model with external field

We numerically investigate the three-dimensional O(6) model on 12^3 to 120^3 lattices. From Binder's cumulant at vanishing magnetic field we obtain the critical coupling J_c=1.42865(5) and verify this value with the \chi^2-method. The universal value of Binder's cumulant at this point is g_r(J_c)=-1.94456(10). At the critical coupling we find the critical exponents \nu=0.818(5), \beta=0.425(2) and \gamma=1.604(6) from a finite size scaling analysis. We also determine the finite-size-scaling function on the critical line and the equation of state. Our O(6)-result for the equation of state is compared to the Ising, O(2) and O(4) results.Comment: 5 pages, 4 figures, To appear in the proceedings of Workshop on Strong and Electroweak Matter (SEWM 2002), Heidelberg, Germany, 2-5 Oct 200

The Nonabelian Screening Potential Beyond the Leading Order

The nonabelian screening potential is calculated in the temporal axial gauge. The Slavnov-Taylor identity is used to construct the three-gluon vertex function from the inverse gluon propagator. After solving the Schwinger - Dyson equation beyond leading order we find that the obtained momentum dependence of the gluon self-energy at high temperature does not correspond to an attractive QCD - Debye potential, but instead it is repulsive and power behaved ($\simeq 1/r^6$) at large distance.Comment: 10 pages, LATEX, ( 1 figure not included), BI-TP 94/0

Aufbruch und Begrenzung. 50 Jahre Universität Bielefeld als sich öffnender Raum für Frauen

Grau J, Plöger L, Universität Bielefeld, eds. Aufbruch und Begrenzung. 50 Jahre Universität Bielefeld als sich öffnender Raum für Frauen. Bielefeld: Universität Bielefeld; 2019