35,301 research outputs found

    Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants

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    We study the effects of failure to equilibrate the squared topological charge Q2Q^2 on lattice calculations of pseudoscalar masses and decay constants. The analysis is based on chiral perturbation theory calculations of the dependence of these quantities on the QCD vacuum angle θ\theta. For the light-light partially quenched case, we rederive the known chiral perturbation theory results of Aoki and Fukaya, but using the nonperturbatively-valid chiral theory worked out by Golterman, Sharpe and Singleton, and by Sharpe and Shoresh. We then extend these calculations to heavy-light mesons. Results when staggered taste-violations are important are also presented. The derived Q2Q^2 dependence is compared to that of simulations using the MILC collaboration's ensembles of lattices with four flavors of HISQ dynamical quarks. We find agreement, albeit with large statistical errors. These results can be used to correct for the leading effects of unequilibrated Q2Q^2, or to make estimates of the systematic error coming from the failure to equilibrate Q2Q^2. In an appendix, we show that the partially quenched chiral theory may be extended beyond a lower bound on valence masses discovered by Sharpe and Shoresh. Subtleties occurring when a sea-quark mass vanishes are discussed in another appendix.Comment: 46 pages, 5 figures; added section on the effect of staggered taste violations and made other improvements for clarity. Version to be published in Phys. Rev.

    Maximal entropy random networks with given degree distribution

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    Using a maximum entropy principle to assign a statistical weight to any graph, we introduce a model of random graphs with arbitrary degree distribution in the framework of standard statistical mechanics. We compute the free energy and the distribution of connected components. We determine the size of the percolation cluster above the percolation threshold. The conditional degree distribution on the percolation cluster is also given. We briefly present the analogous discussion for oriented graphs, giving for example the percolation criterion.Comment: 22 pages, LateX, no figur

    A One Dimensional Ideal Gas of Spinons, or Some Exact Results on the XXX Spin Chain with Long Range Interaction

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    We describe a few properties of the XXX spin chain with long range interaction. The plan of these notes is: 1. The Hamiltonian 2. Symmetry of the model 3. The irreducible multiplets 4. The spectrum 5. Wave functions and statistics 6. The spinon description 7. The thermodynamicsComment: Latex. Talk given by the first author at the Cargese-1993 workshop "Strings, conformal models and Topological felds theorie

    Errata for: Differential Equations for Sine-Gordon Correlation Functions at the Free Fermion Point

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    We present some important corrections to our work which appeared in Nucl. Phys. B426 (1994) 534 (hep-th/9402144). Our previous results for the correlation functions ⟨eiαΦ(x)eiα′Φ(0)⟩\langle e^{i\alpha \Phi(x)} e^{i\alpha' \Phi (0) } \rangle were only valid for α=α′\alpha = \alpha', due to the fact that we didn't find the most general solution to the differential equations we derived. Here we present the solution corresponding to α≠α′\alpha \neq \alpha'.Comment: 4 page

    Poisson algebra of 2d dimensionally reduced gravity

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    Using a Lax pair based on twisted affine sl(2,R)sl(2,R) Kac-Moody and Virasoro algebras, we deduce a r-matrix formulation of two dimensional reduced vacuum Einstein's equations. Whereas the fundamental Poisson brackets are non-ultralocal, they lead to pure c-number modified Yang-Baxter equations. We also describe how to obtain classical observables by imposing reasonable boundaries conditions.Comment: 16 pages, minor corrections. To appear in JHE
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