Large N lattice QCD and its extended strong-weak connection to the hypersphere

We calculate an effective Polyakov line action of QCD at large Nc and large Nf from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S^1 x S^d at weak coupling from one loop perturbation theory, and find that a large Nc correspondence of equations of motion found in \cite{Hollowood:2012nr} at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for computing higher order corrections to the lattice effective action, in order to make higher order comparisons more straightforward.Comment: 33 pages, 7 figure

Calculating the chiral condensate diagrammatically at strong coupling

We calculate the chiral condensate of QCD at infinite coupling as a function of the number of fundamental fermion flavours using a lattice diagrammatic approach inspired by recent work of Tomboulis, and other work from the 80's. We outline the approach where the diagrams are formed by combining a truncated number of sub-diagram types in all possible ways. Our results show evidence of convergence and agreement with simulation results at small Nf. However, contrary to recent simulation results, we do not observe a transition at a critical value of Nf. We further present preliminary results for the chiral condensate of QCD with symmetric or adjoint representation fermions at infinite coupling as a function of Nf for Nc = 3. In general, there are sources of error in this approach associated with miscounting of overlapping diagrams, and over-counting of diagrams due to symmetries. These are further elaborated upon in a longer paper.Comment: presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, New York, NY, US

Three-dimensional images of choanoflagellate loricae

Choanoflagellates are unicellular filter-feeding protozoa distributed universally in aquatic habitats. Cells are ovoid in shape with a single anterior flagellum encircled by a funnel-shaped collar of microvilli. Movement of the flagellum creates water currents from which food particles are entrapped on the outer surface of the collar and ingested by pseudopodia. One group of marine choanoflagellates has evolved an elaborate basket-like exoskeleton, the lorica, comprising two layers of siliceous costae made up of costal strips. A computer graphic model has been developed for generating three-dimensional images of choanoflagellate loricae based on a universal set of 'rules' derived from electron microscopical observations. This model has proved seminal in understanding how complex costal patterns can be assembled in a single continuous movement. The lorica, which provides a rigid framework around the cell, is multifunctional. It resists the locomotory forces generated by flagellar movement, directs and enhances water flow over the collar and, for planktonic species, contributes towards maintaining cells in suspension. Since the functional morphology of choanoflagellate cells is so effective and has been highly conserved within the group, the ecological and evolutionary radiation of choanoflagellates is almost entirely dependent on the ability of the external coverings, particularly the lorica, to diversify

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Possible origin of 60-K plateau in the YBa2Cu3O(6+y) phase diagram

We study a model of YBa2Cu3O(6+y) to investigate the influence of oxygen ordering and doping imbalance on the critical temperature Tc(y) and to elucidate a possible origin of well-known feature of YBCO phase diagram: the 60-K plateau. Focusing on "phase only" description of the high-temperature superconducting system in terms of collective variables we utilize a three-dimensional semi microscopic XY model with two-component vectors that involve phase variables and adjustable parameters representing microscopic phase stiffnesses. The model captures characteristic energy scales present in YBCO and allows for strong anisotropy within basal planes to simulate oxygen ordering. Applying spherical closure relation we have solved the phase XY model with the help of transfer matrix method and calculated Tc for chosen system parameters. Furthermore, we investigate the influence of oxygen ordering and doping imbalance on the shape of YBCO phase diagram. We find it unlikely that oxygen ordering alone can be responsible for the existence of 60-K plateau. Relying on experimental data unveiling that oxygen doping of YBCO may introduce significant charge imbalance between CuO2 planes and other sites, we show that simultaneously the former are underdoped, while the latter -- strongly overdoped almost in the whole region of oxygen doping in which YBCO is superconducting. As a result, while oxygen content is increased, this provides two counter acting factors, which possibly lead to rise of 60K plateau. Additionally, our result can provide an important contribution to understanding of experimental data supporting existence of multicomponent superconductivity in YBCO.Comment: 9 pages, 8 figures, submitted to PRB, see http://prb.aps.or

Category-length and category-strength effects using images of scenes

Global matching models have provided an important theoretical framework for recognition memory. Key predictions of this class of models are that (1) increasing the number of occurrences in a study list of some items affects the performance on other items (list-strength effect) and that (2) adding new items results in a deterioration of performance on the other items (list-length effect). Experimental confirmation of these predictions has been difficult, and the results have been inconsistent. A review of the existing literature, however, suggests that robust length and strength effects do occur when sufficiently similar hard-to-label items are used. In an effort to investigate this further, we had participants study lists containing one or more members of visual scene categories (bathrooms, beaches, etc.). Experiments 1 and 2 replicated and extended previous findings showing that the study of additional category members decreased accuracy, providing confirmation of the category-length effect. Experiment 3 showed that repeating some category members decreased the accuracy of nonrepeated members, providing evidence for a category-strength effect. Experiment 4 eliminated a potential challenge to these results. Taken together, these findings provide robust support for global matching models of recognition memory. The overall list lengths, the category sizes, and the number of repetitions used demonstrated that scene categories are well-suited to testing the fundamental assumptions of global matching models. These include (A) interference from memories for similar items and contexts, (B) nondestructive interference, and (C) that conjunctive information is made available through a matching operation

Multiphase PC/PL Relations: Comparison between Theory and observations

Cepheids are fundamental objects astrophysically in that they hold the key to a CMB independent estimate of Hubble's constant. A number of researchers have pointed out the possibilities of breaking degeneracies between Omega_Matter and H0 if there is a CMB independent distance scale accurate to a few percent (Hu 2005). Current uncertainties in the distance scale are about 10% but future observations, with, for example, the JWST, will be capable of estimating H0 to within a few percent. A crucial step in this process is the Cepheid PL relation. Recent evidence has emerged that the PL relation, at least in optical bands, is nonlinear and that neglect of such a nonlinearity can lead to errors in estimating H0 of up to 2 percent. Hence it is important to critically examine this possible nonlinearity both observationally and theoretically. Existing PC/PL relations rely exclusively on evaluating these relations at mean light. However, since such relations are the average of relations at different phases. Here we report on recent attempts to compare theory and observation in the multiphase PC/PL planes. We construct state of the art Cepheid pulsations models appropriate for the LMC/Galaxy and compare the resulting PC/PL relations as a function of phase with observations. For the LMC, the (V-I) period-color relation at minimum light can have quite a narrow dispersion (0.2-0.3 mags) and thus could be useful in placing constraints on models. At longer periods, the models predict significantly redder (by about 0.2-0.3 mags) V-I colors. We discuss possible reasons for this and also compare PL relations at various phases of pulsation and find clear evidence in both theory and observations for a nonlinear PL relation.Comment: 5 pages, 8 figures, proceeding for "Stellar Pulsation: Challenges for Theory and Observation", Santa Fe 200

Non-perturbative corrections to mean-field behavior: spherical model on spider-web graph

We consider the spherical model on a spider-web graph. This graph is effectively infinite-dimensional, similar to the Bethe lattice, but has loops. We show that these lead to non-trivial corrections to the simple mean-field behavior. We first determine all normal modes of the coupled springs problem on this graph, using its large symmetry group. In the thermodynamic limit, the spectrum is a set of $\delta$-functions, and all the modes are localized. The fractional number of modes with frequency less than $\omega$ varies as $\exp (-C/\omega)$ for $\omega$ tending to zero, where $C$ is a constant. For an unbiased random walk on the vertices of this graph, this implies that the probability of return to the origin at time $t$ varies as $\exp(- C' t^{1/3})$, for large $t$, where $C'$ is a constant. For the spherical model, we show that while the critical exponents take the values expected from the mean-field theory, the free-energy per site at temperature $T$, near and above the critical temperature $T_c$, also has an essential singularity of the type $\exp[ -K {(T - T_c)}^{-1/2}]$.Comment: substantially revised, a section adde