42,180 research outputs found
Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants
We study the effects of failure to equilibrate the squared topological charge
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 . 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 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 , or to make estimates of the systematic
error coming from the failure to equilibrate . 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
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 Classification of random Dirac fermions
We present a detailed classification of random Dirac hamiltonians in two
spatial dimensions based on the implementation of discrete symmetries. Our
classification is slightly finer than that of random matrices, and contains
thirteen classes. We also extend this classification to non-hermitian
hamiltonians with and without Dirac structure.Comment: 15 pages, version2: typos in the table of classes are correcte
Dressing Symmetries
We study Lie-Poisson actions on symplectic manifolds. We show that they are
generated by non-Abelian Hamiltonians. We apply this result to the group of
dressing transformations in soliton theories; we find that the non-Abelian
Hamiltonian is just the monodromy matrix. This provides a new proof of their
Lie-Poisson property. We show that the dressing transformations are the
classical precursors of the non-local and quantum group symmetries of these
theories. We treat in detail the examples of the Toda field theories and the
Heisenberg model.Comment: (29 pages
A One Dimensional Ideal Gas of Spinons, or Some Exact Results on the XXX Spin Chain with Long Range Interaction
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
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