74 research outputs found
Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. V. Further Results for the Square-Lattice Chromatic Polynomial
We derive some new structural results for the transfer matrix of
square-lattice Potts models with free and cylindrical boundary conditions. In
particular, we obtain explicit closed-form expressions for the dominant (at
large |q|) diagonal entry in the transfer matrix, for arbitrary widths m, as
the solution of a special one-dimensional polymer model. We also obtain the
large-q expansion of the bulk and surface (resp. corner) free energies for the
zero-temperature antiferromagnet (= chromatic polynomial) through order q^{-47}
(resp. q^{-46}). Finally, we compute chromatic roots for strips of widths 9 <=
m <= 12 with free boundary conditions and locate roughly the limiting curves.Comment: 111 pages (LaTeX2e). Includes tex file, three sty files, and 19
Postscript figures. Also included are Mathematica files data_CYL.m and
data_FREE.m. Many changes from version 1: new material on series expansions
and their analysis, and several proofs of previously conjectured results.
Final version to be published in J. Stat. Phy
Spanning forests and the q-state Potts model in the limit q \to 0
We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta
J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially,
this limit gives rise to the generating polynomial of spanning forests;
physically, it provides information about the Potts-model phase diagram in the
neighborhood of (q,v) = (0,0). We have studied this model on the square and
triangular lattices, using a transfer-matrix approach at both real and complex
values of w. For both lattices, we have computed the symbolic transfer matrices
for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves
of partition-function zeros in the complex w-plane. For real w, we find two
distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp.
w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w >
w_0 we find a non-critical disordered phase, while for w < w_0 our results are
compatible with a massless Berker-Kadanoff phase with conformal charge c = -2
and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w =
w_0 we find a "first-order critical point": the first derivative of the free
energy is discontinuous at w_0, while the correlation length diverges as w
\downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0
seems to be the same for both lattices and it differs from that of the
Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1,
the leading thermal scaling dimension is x_{T,1} = 0, and the critical
exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65
Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and
forests_tri_2-9P.m. Final journal versio
Beam-energy Dependence Of Charge Balance Functions From Au + Au Collisions At Energies Available At The Bnl Relativistic Heavy Ion Collider
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Balance functions have been measured in terms of relative pseudorapidity (Δη) for charged particle pairs at the BNL Relativistic Heavy Ion Collider from Au + Au collisions at sNN=7.7GeV to 200 GeV using the STAR detector. These results are compared with balance functions measured at the CERN Large Hadron Collider from Pb + Pb collisions at sNN=2.76TeV by the ALICE Collaboration. The width of the balance function decreases as the collisions become more central and as the beam energy is increased. In contrast, the widths of the balance functions calculated using shuffled events show little dependence on centrality or beam energy and are larger than the observed widths. Balance function widths calculated using events generated by UrQMD are wider than the measured widths in central collisions and show little centrality dependence. The measured widths of the balance functions in central collisions are consistent with the delayed hadronization of a deconfined quark gluon plasma (QGP). The narrowing of the balance function in central collisions at sNN=7.7 GeV implies that a QGP is still being created at this relatively low energy. © 2016 American Physical Society.942CNPq, Conselho Nacional de Desenvolvimento Científico e TecnológicoMinistry of Education and Science of the Russian FederationMOE, Ministry of Education of the People's Republic of ChinaMOST, Ministry of Science and Technology of the People's Republic of ChinaNRF-2012004024, National Research FoundationNSF, National Stroke FoundationConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq
J/ψ Production At Low Pt In Au+au And Cu+cu Collisions At Snn =200 Gev With The Star Detector
The J/ψ pT spectrum and nuclear modification factor (RAA) are reported for pT<5GeV/c and |y|<1 from 0% to 60% central Au+Au and Cu+Cu collisions at sNN=200GeV at STAR. A significant suppression of pT-integrated J/ψ production is observed in central Au+Au events. The Cu+Cu data are consistent with no suppression, although the precision is limited by the available statistics. RAA in Au+Au collisions exhibits a strong suppression at low transverse momentum and gradually increases with pT. The data are compared to high-pT STAR results and previously published BNL Relativistic Heavy Ion Collider results. Comparing with model calculations, it is found that the invariant yields at low pT are significantly above hydrodynamic flow predictions but are consistent with models that include color screening and regeneration. © 2014 American Physical Society.902CNRS/IN2P3; NSF; Arthritis National Research Foundation; NRF-2012004024; ANRF; Arthritis National Research FoundationMatsui, T., Satz, H., (1986) Phys Lett. B, 178, p. 416. , PYLBAJ 0370-2693 10.1016/0370-2693(86)91404-8Digal, S., Petreczky, P., Satz, H., (2001) Phys. Rev. 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Measurement Of Charge Multiplicity Asymmetry Correlations In High-energy Nucleus-nucleus Collisions At Snn =200 Gev
A study is reported of the same- and opposite-sign charge-dependent azimuthal correlations with respect to the event plane in Au+Au collisions at sNN=200 GeV. The charge multiplicity asymmetries between the up/down and left/right hemispheres relative to the event plane are utilized. The contributions from statistical fluctuations and detector effects were subtracted from the (co-)variance of the observed charge multiplicity asymmetries. In the mid- to most-central collisions, the same- (opposite-) sign pairs are preferentially emitted in back-to-back (aligned on the same-side) directions. The charge separation across the event plane, measured by the difference, Δ, between the like- and unlike-sign up/down-left/right correlations, is largest near the event plane. 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Electron and photon energy calibration with the ATLAS detector using LHC Run 2 data
This paper presents the electron and photon energy calibration obtained with the ATLAS detector using 140 fb-1 of LHC proton-proton collision data recorded at √(s) = 13 TeV between 2015 and 2018. Methods for the measurement of electron and photon energies are outlined, along with the current knowledge of the passive material in front of the ATLAS electromagnetic calorimeter. The energy calibration steps are discussed in detail, with emphasis on the improvements introduced in this paper. The absolute energy scale is set using a large sample of Z-boson decays into electron-positron pairs, and its residual dependence on the electron energy is used for the first time to further constrain systematic uncertainties. The achieved calibration uncertainties are typically 0.05% for electrons from resonant Z-boson decays, 0.4% at ET ∼ 10 GeV, and 0.3% at ET ∼ 1 TeV; for photons at ET ∼ 60 GeV, they are 0.2% on average. This is more than twice as precise as the previous calibration. The new energy calibration is validated using J/ψ → ee and radiative Z-boson decays
Performance and calibration of quark/gluon-jet taggers using 140 fb−1 of pp collisions at √s = 13 TeV with the ATLAS detector
The identification of jets originating from quarks and gluons, often referred to as quark/gluon tagging, plays an important role in various analyses performed at the Large Hadron Collider, as Standard Model measurements and searches for new particles decaying to quarks often rely on suppressing a large gluon-induced background. This paper describes the measurement of the efficiencies of quark/gluon taggers developed within the ATLAS Collaboration, using √s = 13 TeV proton–proton collision data with an integrated luminosity of 140 fb-1 collected by the ATLAS experiment. Two taggers with high performances in rejecting jets from gluon over jets from quarks are studied: one tagger is based on requirements on the number of inner-detector tracks associated with the jet, and the other combines several jet substructure observables using a boosted decision tree. A method is established to determine the quark/gluon fraction in data, by using quark/gluon-enriched subsamples defined by the jet pseudorapidity. Differences in tagging efficiency between data and simulation are provided for jets with transverse momentum between 500 GeV and 2 TeV and for multiple tagger working points
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